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Introduction and Data Collection

CHAPTER 1: INTRODUCTION AND DATA COLLECTION 1. The process of using sample statistics to draw conclusions about true population parameters is called a) statistical inference. b) the scientific method. c) sampling. d) descriptive statistics. ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: inferential statistics 2. Those methods involving the collection, presentation, and characterization of a set of data in order to properly describe the various features of that set of data are called a) statistical inference. b) the scientific method. c) sampling. d) descriptive statistics. ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: descriptive statistics 3. The collection and summarization of the socioeconomic and physical characteristics of the employees of a particular firm is an example of a) inferential statistics. b) descriptive statistics. c) a parameter. d) a statistic. ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: descriptive statistics 4. The estimation of the population average family expenditure on food based on the sample average expenditure of 1,000 families is an example of a) inferential statistics. b) descriptive statistics. c) a parameter. d) a statistic. ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: inferential statistics

Introduction and Data Collection 5. The universe or "totality of items or things" under consideration is called a) a sample. b) a population. c) a parameter. d) a statistic. ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: population 6.

The portion of the universe that has been selected for analysis is called a) a sample. b) a frame. c) a parameter. d) a statistic.

ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: sample 7. A summary measure that is computed to describe a characteristic from only a sample of the population is called a) a parameter. b) a census. c) a statistic. d) the scientific method. ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: statistic 8. A summary measure that is computed to describe a characteristic of an entire population is called a) a parameter. b) a census. c) a statistic. d) the scientific method. ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: parameter 9. Which of the following is most likely a population as opposed to a sample? a) respondents to a newspaper survey b) the first 5 students completing an assignment c) every third person to arrive at the bank d) registered voters in a county ANSWER: d

Introduction and Data Collection TYPE: MC DIFFICULTY: Moderate KEYWORDS: population, sample 10. Which of the following is most likely a parameter as opposed to a statistic? a) the average score of the first five students completing an assignment b) the proportion of females registered to vote in a county c) the average height of people randomly selected from a database d) the proportion of trucks stopped yesterday that were cited for bad brakes ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: parameter, statistic 11. Which of the following is not an element of descriptive statistical problems? a) an inference made about the population based on the sample b) the population or sample of interest c) tables, graphs, or numerical summary tools d) identification of patterns in the data ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: descriptive statistics

12. A study is under way in Yosemite National Forest to determine the adult height of American pine trees. Specifically, the study is attempting to determine what factors aid a tree in reaching heights greater than 60 feet tall. It is estimated that the forest contains 25,000 adult American pines. The study involves collecting heights from 250 randomly selected adult American pine trees and analyzing the results. Identify the population from which the study was sampled. a) the 250 randomly selected adult American pine trees b) the 25,000 adult American pine trees in the forest c) all the adult American pine trees taller than 60 feet d) all American pine trees, of any age, in the forest ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: population, sample

13. A study is under way in Yosemite National Forest to determine the adult height of American pine trees. Specifically, the study is attempting to determine what factors aid a tree in reaching heights greater than 60 feet tall. It is estimated that the forest contains 25,000 adult American pines. The study involves collecting heights from 250 randomly selected adult American pine trees and analyzing the results. Identify the variable of interest in the study a) the age of an American pine tree in Yosemite National Forest b) the height of an American pine tree in Yosemite National Forest c) the number of American pine trees in Yosemite National Forest d) the species of trees in Yosemite National Forest ANSWER: b

Introduction and Data Collection TYPE: MC DIFFICULTY: Easy KEYWORDS: data, sampling 14. A study is under way in Yosemite National Forest to determine the adult height of American pine trees. Specifically, the study is attempting to determine what factors aid a tree in reaching heights greater than 60 feet tall. It is estimated that the forest contains 25,000 adult American pines. The study involves collecting heights from 250 randomly selected adult American pine trees and analyzing the results. Identify the sample in the study. a) the 250 randomly selected adult American pine trees b) the 25,000 adult American pine trees in the forest c) all the adult American pine trees taller than 60 feet d) all American pine trees, of any age, in the forest ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: population, sample 15. Most analysts focus on the cost of tuition as the way to measure the cost of a college education. But incidentals, such as textbook costs, are rarely considered. A researcher at Drummand University wishes to estimate the textbook costs of first-year students at Drummand. To do so, she monitored the textbook cost of 250 first-year students and found that their average textbook cost was $300 per semester. Identify the population of interest to the researcher. a) all Drummand University students b) all college students c) all first-year Drummand University students d) the 250 students that were monitored ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: population, sample 16. Most analysts focus on the cost of tuition as the way to measure the cost of a college education. But incidentals, such as textbook costs, are rarely considered. A researcher at Drummand University wishes to estimate the textbook costs of first-year students at Drummand. To do so, she monitored the textbook cost of 250 first-year students and found that their average textbook cost was $300 per semester. Identify the variable of interest to the researcher a) the textbook cost of first-year Drummand University students b) the year in school of Drummand University students c) the age of Drummand University students d) the cost of incidental expenses of Drummand University students ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: data, sampling 17. Most analysts focus on the cost of tuition as the way to measure the cost of a college education. But incidentals, such as textbook costs, are rarely considered. A researcher at Drummand University wishes to estimate the textbook costs of first-year students at Drummand. To do so, she monitored the textbook cost of 250 first-year students and found that their average textbook cost was $300 per semester. Identify the sample in the study.

Introduction and Data Collection

a) all Drummand University students b) all college students c) all first-year Drummand University students d) the 250 students that were monitored ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: population, sample 18. Researchers suspect that the average number of units earned per semester by college students is rising. A researcher at Calendula College wishes to estimate the number of units earned by students during the spring semester at Calendula. To do so, he randomly selects 100 student transcripts and records the number of units each student earned in the spring term. He found that the average number of semester units completed was 12.96 units per student. Identify the population of interest to the researcher. a) all Calendula College students b) all college students c) all Calendula College students enrolled in the spring d) all college students enrolled in the spring ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: population, sample 19. The average number of units earned per semester by college students is suspected to be rising. A researcher at Calendula College wishes to estimate the number of units earned by students during the spring semester at Calendula. To do so, he randomly selects 100 student transcripts and records the number of units each student earned in the spring term. Identify the variable of interest to the researcher. a) the number of students enrolled at Calendula College during the spring term b) the average indebtedness of Calendula College students enrolled in the spring c) the age of Calendula College students enrolled in the spring d) the number of units earned by Calendula College students during the spring term ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: data, sampling 20. Jared was working on a project to look at global warming and accessed an Internet site where he captured average global surface temperatures from 1866. Which of the four methods of data collection was he using? a) published sources b) experimentation c) surveying d) observation ANSWER: a TYPE: MC DIFFICULTY: Easy

Introduction and Data Collection KEYWORDS: sources of data 21. The British Airways Internet site provides a questionnaire instrument that can be answered electronically. Which of the 4 methods of data collection is involved when people complete the questionnaire? a) published sources b) experimentation c) surveying d) observation ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: sources of data 22. A marketing research firm, in conducting a comparative taste test, provided three types of peanut butter to a sample of households randomly selected within the state. Which of the 4 methods of data collection is involved when people are asked to compare the three types of peanut butter? a) published sources b) experimentation c) surveying d) observation ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: sources of data

23. Tim was planning for a meeting with his boss to discuss a raise in his annual salary. In preparation, he wanted to use the Consumer Price Index to determine the percentage increase in his real (inflation-adjusted) salary over the last three years. Which of the 4 methods of data collection was involved when he used the Consumer Price Index? a) published sources b) experimentation c) surveying d) observation ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: sources of data 24. Which of the 4 methods of data collection is involved when a person counts the number of cars passing designated locations on the Los Angeles freeway system? a) published sources b) experimentation c) surveying d) observation ANSWER: d TYPE: MC DIFFICULTY: Moderate

Introduction and Data Collection

KEYWORDS: sources of data 25. A statistics student found a reference in the campus library that contained the median family incomes for all 50 states. She would report her data as being collected using a) a designed experiment. b) observational data. c) a random sample. d) a published source. ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: sources of data 26. The personnel director at a large company studied the eating habits of the company’s employees. The director noted whether employees brought their own lunches to work, ate at the company cafeteria, or went out to lunch. The goal of the study was to improve the food service at the company cafeteria. This type of data collection would best be considered as a) an observational study. b) a designed experiment. c) a random sample. d) a quota sample. ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: sources of data 27. A study attempted to estimate the proportion of Florida residents who were willing to spend more tax dollars on protecting the beaches from environmental disasters. Twenty-five hundred Florida residents were surveyed. What type of data collection procedure was most likely used to collect the data for this study? a) a designed experiment b) a published source c) a random sample d) observational data ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: sources of data 28. Which of the following is a discrete quantitative variable? a) the Dow Jones Industrial average b) the volume of water released from a dam c) the distance you drove yesterday. d) the number of employees of an insurance company ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: discrete random variable, types of data

Introduction and Data Collection 29. Which of the following is a continuous quantitative variable? a) the color of a student’s eyes b) the number of employees of an insurance company c) the amount of milk produced by a cow in one 24-hour period d) the number of gallons of milk sold at the local grocery store yesterday ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: continuous random variable, types of data

30. To monitor campus security, the campus police office is taking a survey of the number of students in a parking lot each 30 minutes of a 24-hour period with the goal of determining when patrols of the lot would serve the most students. If X is the number of students in the lot each period of time, then X is an example of a) a categorical random variable. b) a discrete random variable. c) a continuous random variable. d) a statistic. ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: discrete random variable, types of data

31. Researchers are concerned that the weight of the average American school child is increasing

implying, among other things, that children’s clothing should be manufactured and marketed in larger sizes. If X is the weight of school children sampled in a nationwide study, then X is an example of a) a categorical random variable. b) a discrete random variable. c) a continuous random variable. d) a parameter.

ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: continuous random variable, types of data 32. The classification of student class designation (freshman, sophomore, junior, senior) is an example of a) a categorical random variable. b) a discrete random variable. c) a continuous random variable. d) a parameter. ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: categorical random variable, types of data 33. The classification of student major (accounting, economics, management, marketing, other) is an example of

Introduction and Data Collection a) b) c) d)

a categorical random variable. a discrete random variable. a continuous random variable. a parameter.

ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: categorical random variable, types of data

34. The chancellor of a major university was concerned about alcohol abuse on her campus and wanted to find out the proportion of students at her university who visited campus bars on the weekend before the final exam week. Her assistant took a random sample of 250 students. The total number of students in the sample who visited campus bars on the weekend before the final exam week is an example of a) a categorical random variable. b) a discrete random variable. c) a continuous random variable. d) a parameter. ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: discrete random variable, types of data

35. The chancellor of a major university was concerned about alcohol abuse on her campus and wanted to find out the proportion of students at her university who visited campus bars on the weekend before the final exam week. Her assistant took a random sample of 250 students and computed the portion of students in the sample who visited campus bars on the weekend before the final exam. The portion of all students at her university who visited campus bars on the weekend before the final exam week is an example of a) a categorical random variable. b) a discrete random variable. c) a continuous random variable. d) a parameter. ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: parameter, types of data

36. The chancellor of a major university was concerned about alcohol abuse on her campus and wanted to find out the proportion of students at her university who visited campus bars on the weekend before the final exam week. Her assistant took a random sample of 250 students. The portion of students in the sample who visited campus bars on the weekend before the final exam week is an example of a) a categorical random variable. b) a discrete random variable. c) a parameter. d) a statistic. ANSWER: d

10 Introduction and Data Collection TYPE: MC DIFFICULTY: Moderate KEYWORDS: statistic, types of data

37. The chancellor of a major university was concerned about alcohol abuse on her campus and wanted to find out the proportion of students at her university who visited campus bars on the weekend before the final exam week. Her assistant took a random sample of 250 students. The portion of students in the sample who visited campus bars on the weekend before the final exam week is an example of a) a categorical random variable. b) a discrete random variable. c) a continuous random variable. d) a parameter. ANSWER: c TYPE: MC DIFFICULTY: Difficult KEYWORDS: continuous random variable, types of data TABLE 1-1 The manager of the customer service division of a major consumer electronics company is interested in determining whether the customers who have purchased a videocassette recorder made by the company over the past 12 months are satisfied with their products. 38. Referring to Table 1-1, the population of interest is a) all the customers who have bought a videocassette recorder made by the company over the past 12 months. b) all the customers who have bought a videocassette recorder made by the company and brought it in for repair over the past 12 months. c) all the customers who have used a videocassette recorder over the past 12 months. d) all the customers who have ever bought a videocassette recorder made by the company. ANSWER: a TYPE: MC DIFFICULTY: Difficult KEYWORDS: population 39. Referring to Table 1-1, the possible responses to the question "How many videocassette recorders made by other manufacturers have you used?" are values from a a) discrete random variable. b) continuous random variable. c) categorical random variable. d) parameter. ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: discrete random variable, types of data 40. Referring to Table 1-1, the possible responses to the question "Are you happy, indifferent, or unhappy with the performance per dollar spent on the videocassette recorder?" are values from a a) discrete numerical random variable. b) continuous numerical random variable. c) categorical random variable.

Introduction and Data Collection

d) parameter. ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: categorical random variable, types of data 41. True or False: A population is the totality of items or things under consideration. ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: population 42. True or False: A sample is the portion of the universe that is selected for analysis. ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: sample 43. True or False: Problems may arise when statistically unsophisticated users who do not understand the assumptions behind the statistical procedures or their limitations are misled by results obtained from computer software. ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: statistical package 44. True or False: Managers need an understanding of statistics to be able to present and describe information accurately, draw conclusions about large populations based on small samples, improve processes, and make reliable forecasts. ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: reasons for learning statistics 45. True or False: The possible responses to the question “How long have you been living at your current residence?” are values from a continuous variable. ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: continuous random variable, types of data 46. True or False: The possible responses to the question “How many times in the past three months have you visited a city park?” are values from a discrete variable. ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: discrete random variable, types of data

12 Introduction and Data Collection

47. True or False: A continuous variable may take on any value within its relevant range even though the measurement device may not be precise enough to record it. ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: continuous random variable, types of data

48. True or False: Faculty rank (professor to lecturer) is an example of discrete numerical data. ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: categorical random variable, types of data 49. True or False: Student grades (A to F) are an example of continuous numerical data. ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: categorical random variables, types of data 50. True or False: The amount of coffee consumed by an individual in a day is an example of a discrete numerical variable. ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: continuous random variables, types of data 51. True or False: A statistic is usually used to provide an estimate for a usually unobserved parameter. ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: statistic, parameter, inferential statistics 52. True or False: A statistic is usually unobservable while a parameter is usually observable. ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: statistic, parameter, inferential statistic 53. True or False: The answer to the question “What is your favorite color?” is an example of an ordinal scaled variable. ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: nominal scale

Introduction and Data Collection

54. True or False: The answer to the question “How do you rate the quality of your business statistics course” is an example of an ordinal scaled variable. ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: ordinal scale 55. True or False: The answer to the question “How many hours on average do you spend watching TV every week?” is an example of a ratio scaled variable. ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: ratio scale 56. True or False: The answer to the question “What is your sleeping bag temperature rating?” is an example of a ratio scaled variable. ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: interval scale

57. The Human Resources Director of a large corporation wishes to develop an employee benefits package and decides to select 500 employees from a list of all (N = 40,000) workers in order to study their preferences for the various components of a potential package. All the employees in the corporation constitute the . ANSWER: population TYPE: FI DIFFICULTY: Easy KEYWORDS: population

58. The Human Resources Director of a large corporation wishes to develop an employee benefits package and decides to select 500 employees from a list of all (N = 40,000) workers in order to study their preferences for the various components of a potential package. The 500 employees who will participate in this study constitute the . ANSWER: sample TYPE: FI DIFFICULTY: Easy KEYWORDS: sample

59. The Human Resources Director of a large corporation wishes to develop an employee benefits package and decides to select 500 employees from a list of all (N = 40,000) workers in order to study their preferences for the various components of a potential package. The Director will use the data from the sample to compute . ANSWER: statistics TYPE: FI DIFFICULTY: Easy KEYWORDS: statistic

14 Introduction and Data Collection

60. The Human Resources Director of a large corporation wishes to develop an employee benefits package and decides to select 500 employees from a list of all (N = 40,000) workers in order to study their preferences for the various components of a potential package. Information obtained from the sample will be used to draw conclusions about the true population . ANSWER: parameters TYPE: FI DIFFICULTY: Easy KEYWORDS: parameter

61. The Human Resources Director of a large corporation wishes to develop an employee benefits package and decides to select 500 employees from a list of all (N = 40,000) workers in order to study their preferences for the various components of a potential package. In this study, methods involving the collection, presentation, and characterization of the data are called . ANSWER: descriptive statistics/methods TYPE: FI DIFFICULTY: Easy KEYWORDS: descriptive statistics

62. The Human Resources Director of a large corporation wishes to develop an employee benefits package and decides to select 500 employees from a list of all (N = 40,000) workers in order to study their preferences for the various components of a potential package. In this study, methods that result in decisions concerning population characteristics based only on the sample results are called . ANSWER: inferential statistics/methods TYPE: FI DIFFICULTY: Easy KEYWORDS: inferential statistics 63. Mediterranean fruit flies were discovered in California a few years ago and badly damaged the oranges grown in that state. Suppose the manager of a large farm wanted to study the impact of the fruit flies on the orange crops on a daily basis over a 6-week period. On each day a random sample of orange trees were selected from within a random sample of acres. The daily average number of damaged oranges per tree and the proportion of trees having damaged oranges were calculated. The two main measures calculated each day (i.e., average number of damaged oranges per tree and proportion of trees having damaged oranges) are called . ANSWER: statistics TYPE: FI DIFFICULTY: Moderate KEYWORDS: statistic 64. Mediterranean fruit flies were discovered in California a few years ago and badly damaged the oranges grown in that state. Suppose the manager of a large farm wanted to study the impact of the fruit flies on the orange crops on a daily basis over a 6-week period. On each day a random sample of orange trees were selected from within a random sample of acres. The daily average number of damaged oranges per tree and the proportion of trees having damaged oranges were calculated. The two main measures calculated each day (i.e., average number of damaged oranges per tree and proportion of trees having damaged oranges) may be used on a daily basis to estimate the respective true population .

Introduction and Data Collection

ANSWER: parameters TYPE: FI DIFFICULTY: Easy KEYWORDS: parameters 65. Mediterranean fruit flies were discovered in California a few years ago and badly damaged the oranges grown in that state. Suppose the manager of a large farm wanted to study the impact of the fruit flies on the orange crops on a daily basis over a 6-week period. On each day a random sample of orange trees were selected from within a random sample of acres. The daily average number of damaged oranges per tree and the proportion of trees having damaged oranges were calculated. In this study, drawing conclusions on any one day about the true population characteristics based on information obtained from the sample is called . ANSWER: inferential statistics/methods TYPE: FI DIFFICULTY: Moderate KEYWORDS: inferential statistics 66. Mediterranean fruit flies were discovered in California a few years ago and badly damaged the oranges grown in that state. Suppose the manager of a large farm wanted to study the impact of the fruit flies on the orange crops on a daily basis over a 6-week period. On each day a random sample of orange trees were selected from within a random sample of acres. The daily average number of damaged oranges per tree and the proportion of trees having damaged oranges were calculated. In this study, the presentation and characterization of the two main measures calculated each day (i.e., average number of damaged oranges per tree and proportion of trees having damaged oranges) is called . ANSWER: descriptive statistics/methods TYPE: FI DIFFICULTY: Moderate KEYWORDS: descriptive statistics 67. The Quality Assurance Department of a large urban hospital is attempting to monitor and evaluate patient satisfaction with hospital services. Prior to discharge, a random sample of patients is asked to fill out a questionnaire to rate such services as medical care, nursing, therapy, laboratory, food, and cleaning. The Quality Assurance Department prepares weekly reports that are presented at the Board of Directors meetings and extraordinary/atypical ratings are easy to flag. Values computed from the sample results each week are called . ANSWER: statistics TYPE: FI DIFFICULTY: Easy KEYWORDS: statistic 68. The Quality Assurance Department of a large urban hospital is attempting to monitor and evaluate patient satisfaction with hospital services. Prior to discharge, a random sample of patients is asked to fill out a questionnaire to rate such services as medical care, nursing, therapy, laboratory, food, and cleaning. The Quality Assurance Department prepares weekly reports that are presented at the Board of Directors meetings and extraordinary/atypical ratings are easy to flag. True population characteristics estimated from the sample results each week are called . ANSWER:

16 Introduction and Data Collection parameters TYPE: FI DIFFICULTY: Easy KEYWORDS: parameter 69. The Commissioner of Health in New York State wanted to study malpractice litigation in New York. A sample of 31 thousand medical records was drawn from a population of 2.7 million patients who were discharged during the year 1997. The proportion of malpractice claims filed from the sample of 31 thousand patients is a . ANSWER: statistic TYPE: FI DIFFICULTY: Moderate KEYWORDS: statistic 70. The Commissioner of Health in New York State wanted to study malpractice litigation in New York. A sample of 31 thousand medical records was drawn from a population of 2.7 million patients who were discharged during the year 1997. The true proportion of malpractice claims filed from the population of 2.7 million patients is a . ANSWER: parameter TYPE: FI DIFFICULTY: Easy KEYWORDS: parameter 71. The Commissioner of Health in New York State wanted to study malpractice litigation in New York. A sample of 31 thousand medical records was drawn from a population of 2.7 million patients who were discharged during the year 1997. Using the information obtained from the sample to predict population characteristics with respect to malpractice litigation is an example of . ANSWER: inferential statistics TYPE: FI DIFFICULTY: Moderate KEYWORDS: inferential statistics 72. The Commissioner of Health in New York State wanted to study malpractice litigation in New York. A sample of 31 thousand medical records was drawn from a population of 2.7 million patients who were discharged during the year 1997. The collection, presentation, and characterization of the data from patient medical records are examples of . ANSWER: descriptive statistics/methods TYPE: FI DIFFICULTY: Easy KEYWORDS: descriptive statistics 73. An insurance company evaluates many numerical variables about a person before deciding on an appropriate rate for automobile insurance. The number of claims a person has made in the last 3 years is an example of a variable. ANSWER: discrete TYPE: FI DIFFICULTY: Easy KEYWORDS: discrete random variable, types of data

Introduction and Data Collection

74. An insurance company evaluates many numerical variables about a person before deciding on an appropriate rate for automobile insurance. The distance a person drives in a year is an example of a variable. ANSWER: continuous TYPE: FI DIFFICULTY: Easy KEYWORDS: continuous random variable, types of data 75. An insurance company evaluates many numerical variables about a person before deciding on an appropriate rate for automobile insurance. A person's age is an example of a variable. ANSWER: continuous TYPE: FI DIFFICULTY: Easy KEYWORDS: continuous random variable, types of data 76. An insurance company evaluates many numerical variables about a person before deciding on an appropriate rate for automobile insurance. How long a person has been a licensed driver is an example of a variable. ANSWER: continuous TYPE: FI DIFFICULTY: Moderate KEYWORDS: continuous random variable, types of data 77. An insurance company evaluates many numerical variables about a person before deciding on an appropriate rate for automobile insurance. The number of tickets a person has received in the last 3 years is an example of a variable. ANSWER: discrete TYPE: FI DIFFICULTY: Easy KEYWORDS: discrete random variable, types of data 78. In purchasing an automobile, there are a number of variables to consider. The body style of the car (sedan, coupe, wagon, etc.) is an example of a variable. ANSWER: categorical TYPE: FI DIFFICULTY: Easy KEYWORDS: categorical random variable, types of data 79. In purchasing an automobile, there are a number of variables to consider. The classification of the car as a subcompact, compact, standard, or luxury size is an example of a variable. ANSWER: categorical TYPE: FI DIFFICULTY: Easy KEYWORDS: categorical random variable, types of data 80. In purchasing an automobile, there are a number of variables to consider. The color of the car is an example of a variable.

18 Introduction and Data Collection ANSWER: categorical TYPE: FI DIFFICULTY: Easy KEYWORDS: categorical random variable, types of data 81. Most colleges admit students based on their achievements in a number of different areas. Whether a student has taken any advanced placement courses is an example of a variable. ANSWER: categorical TYPE: FI DIFFICULTY: Easy KEYWORDS: categorical random variable, types of data 82. Most colleges admit students based on their achievements in a number of different areas. The grade obtained in senior level English. (A, B, C, D, or F) is an example of a variable. ANSWER: categorical TYPE: FI DIFFICULTY: Moderate KEYWORDS: categorical random variable, types of data 83. Most colleges admit students based on their achievements in a number of different areas. The total SAT score achieved by a student is an example of a numerical variable. ANSWER: discrete TYPE: FI DIFFICULTY: Moderate KEYWORDS: discrete random variable, types of data 84. The Dean of Students conducted a survey on campus. The gender of the student is an example of a variable. ANSWER: categorical TYPE: FI DIFFICULTY: Easy KEYWORDS: categorical random variable, types of data 85. The Dean of Students conducted a survey on campus. Class designation (Freshman, Sophomore, Junior, Senior) is an example of a variable. ANSWER: categorical TYPE: FI DIFFICULTY: Easy KEYWORDS: categorical random variable, types of data 86. The Dean of Students conducted a survey on campus. Major area of study is an example of a variable. ANSWER: categorical TYPE: FI DIFFICULTY: Easy KEYWORDS: categorical random variable, types of data

Introduction and Data Collection

87. The Dean of Students conducted a survey on campus. Average SAT score in mathematics is an example of a numerical variable. ANSWER: continuous TYPE: FI DIFFICULTY: Easy KEYWORDS: continuous random variable, types of data 88. The Dean of Students conducted a survey on campus. Grade point average (GPA) is an example of a numerical variable. ANSWER: continuous TYPE: FI DIFFICULTY: Easy KEYWORDS: continuous random variable, types of data 89. The Dean of Students conducted a survey on campus. Number of credits currently enrolled for is an example of a numerical variable. ANSWER: discrete TYPE: FI DIFFICULTY: Easy KEYWORDS: discrete random variable, types of data 90. The Dean of Students conducted a survey on campus. Number of clubs, groups, teams, and organizations affiliated with on campus is an example of a numerical variable. ANSWER: discrete TYPE: FI DIFFICULTY: Easy KEYWORDS: discrete random variable, types of data 91. A personal computer user survey was conducted. Computer brand primarily used is an example of a variable. ANSWER: categorical TYPE: FI DIFFICULTY: Easy KEYWORDS: categorical random variable, types of data

92. A personal computer user survey was conducted. Number of personal computers owned is an example of a

variable.

ANSWER: discrete TYPE: FI DIFFICULTY: Easy KEYWORDS: discrete random variable, types of data 93. A personal computer user survey was conducted. The number of years using a personal computer is an example of a variable. ANSWER: continuous TYPE: FI DIFFICULTY: Moderate

20 Introduction and Data Collection KEYWORDS: continuous random variable, types of data 94. A personal computer user survey was conducted. Hours of personal computer use per week is an example of a variable ANSWER: continuous TYPE: FI DIFFICULTY: Moderate KEYWORDS: continuous random variable, types of data 95. A personal computer user survey was conducted. Primary word processing package used is an example of a variable ANSWER: categorical TYPE: FI DIFFICULTY: Easy KEYWORDS: categorical random variable, types of data 96. A personal computer user survey was conducted. The number of computer magazine subscriptions is an example of a variable. ANSWER: discrete TYPE: FI DIFFICULTY: Moderate KEYWORDS: discrete random variable, types of data 97. The type of TV one owns is an example of an ordinal scaled variable. ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: nominal scale, ordinal scale

98. The type of TV one owns is an example of a numerical variable. ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: categorical random variable 99. Whether the university is private or public is an example of a nominal scaled variable. ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: nominal scale 100.

Whether the university is private or public is an example of a categorical variable.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: categorical random variable

Introduction and Data Collection 101.

Marital status is an example of an ordinal scaled variable.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: nominal scale, ordinal scale 102.

Marital status is an example of a numerical variable.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: categorical random variable

103. The grade level (K-12) of a student is an example of a nominal scaled variable. ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: nominal scale, ordinal scale

104. The grade level (K-12) of a student is an example of a numerical variable. ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: categorical random variable

105. The level of satisfaction (“Very unsatisfied”, “Fairly unsatisfied”, “Fairly satisfied”, and “Very satisfied”) in a class is an example of an ordinal scaled variable.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: ordinal scale

106. The level of satisfaction (“Very unsatisfied”, “Fairly unsatisfied”, “Fairly satisfied”, and “Very satisfied”) in a class is an example of a categorical variable.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: categorical random variable

107. The quality (“terrible”, “poor”, “fair”, “acceptable”, “very good” and “excellent”) of a day care center is an example of a nominal scaled variable. ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: nominal scale, ordinal scale

22 Introduction and Data Collection

108. The quality (“terrible”, “poor”, “fair”, “acceptable”, “very good” and “excellent”) of a day care center is an example of a numerical variable. ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: categorical random variable 109.

The amount of alcohol consumed by a person per week will be measured on an interval scale.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: interval scale, ratio scale 110.

The amount of alcohol consumed by a person per week is an example of a continuous variable.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: continuous random variable 111.

The number of defective apples in a single box will be measured on an interval scale.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: interval scale, ratio scale 112.

The number of defective apples in a single box is an example of a continuous variable.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: discrete random variable, continuous random variable 113. The amount of calories contained in a pack of 12-ounce cheese will be measured on a ratio scale. ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: ratio scale 114. The amount of calories contained in a pack of 12-ounce cheese is an example of a discrete variable. ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: discrete random variable, continuous random variable 115.

The amount of time a student spent studying for an exam will be measured on a ratio scale.

Introduction and Data Collection ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: ratio scale 116. The amount of time a student spent studying for an exam is an example of a continuous variable. ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: continuous random variable 117. The date when a production line in a factor is out-of-control will be measured with a ratio scale. ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: interval scale, ratio scale

26 Presenting Data in Tables and Charts

CHAPTER 2: PRESENTING DATA IN TABLES AND CHARTS TABLE 2-1 An insurance company evaluates many numerical variables about a person before deciding on an appropriate rate for automobile insurance. A representative from a local insurance agency selected a random sample of insured drivers and recorded, X, the number of claims each made in the last 3 years, with the following results. X f 1 14 2 18 3 12 4 5 5 1 1. Referring to Table 2-1, how many drivers are represented in the sample? a) 5 b) 15 c) 18 d) 50 ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: frequency distribution 2. Referring to Table 2-1, how many total claims are represented in the sample? a) 15 b) 50 c) 111 d) 250 ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: interpretation, frequency distribution 3. A type of vertical bar chart in which the categories are plotted in the descending rank order of the magnitude of their frequencies is called a a) contingency table. b) Pareto diagram. c) dot plot. d) pie chart. ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: Pareto diagram

27 Presenting Data in Tables and Charts TABLE 2-2 At a meeting of information systems officers for regional offices of a national company, a survey was taken to determine the number of employees the officers supervise in the operation of their departments, where X is the number of employees overseen by each information systems officer. X f_ 1 7 2 5 3 11 4 8 5 9 4. Referring to Table 2-2, how many regional offices are represented in the survey results? a) 5 b) 11 c) 15 d) 40 ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: interpretation, frequency distribution 5. Referring to Table 2-2, across all of the regional offices, how many total employees were supervised by those surveyed? a) 15 b) 40 c) 127 d) 200 ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: interpretation, frequency distribution 6. The width of each bar in a histogram corresponds to the a) differences between the boundaries of the class. b) number of observations in each class. c) midpoint of each class. d) percentage of observations in each class. ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: frequency distribution TABLE 2-3 Every spring semester, the School of Business coordinates with local business leaders a luncheon for graduating seniors, their families, and friends. Corporate sponsorship pays for the lunches of each of the seniors, but students have to purchase tickets to cover the cost of lunches served to guests they bring with them. The following histogram represents the attendance at the senior luncheon, where X is the number of guests each graduating senior invited to the luncheon and f is the number of graduating seniors in each category.

Presenting Data in Tables and Charts

152

160 140 120 100

80 60 40 20

0 0

2 Guests per Student

7. Referring to the histogram from Table 2-3, how many graduating seniors attended the luncheon? a) 4 b) 152 c) 275 d) 388 ANSWER: c TYPE: MC DIFFICULTY: Difficult EXPLANATION: The number of graduating seniors is the sum of all the frequencies, f. KEYWORDS: interpretation, histogram 8. Referring to the histogram from Table 2-3, if all the tickets purchased were used, how many guests attended the luncheon? a) 4 b) 152 c) 275 d) 388 ANSWER: d TYPE: MC DIFFICULTY: Difficult EXPLANATION: The total number of guests is

 Xf 6

i=1

i i

KEYWORDS: interpretation, histogram 9. A professor of economics at a small Texas university wanted to determine what year in school students were taking his tough economics course. Shown below is a pie chart of the results. What percentage of the class took the course prior to reaching their senior year?

29 Presenting Data in Tables and Charts

Seniors 14%

Freshmen 10%

Juniors 30% Sophomores 46%

a) 14% b) 44% c) 54% d) 86% ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: interpretation, pie chart 10. When polygons or histograms are constructed, which axis must show the true zero or "origin"? a) The horizontal axis. b) The vertical axis. c) Both the horizontal and vertical axes. d) Neither the horizontal nor the vertical axis. ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: polygon, histogram 11. When constructing charts, the following is plotted at the class midpoints: a) frequency histograms b) percentage polygons c) cumulative relative frequency ogives d) All of the above. ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: percentage polygon TABLE 2-4 A survey was conducted to determine how people rated the quality of programming available on television. Respondents were asked to rate the overall quality from 0 (no quality at all) to 100 (extremely good quality). The stem-and-leaf display of the data is shown below. Stem Leaves 3 24 4 03478999 5 0112345

Presenting Data in Tables and Charts

6 7 8 9

12566 01 2

12. Referring to Table 2-4, what percentage of the respondents rated overall television quality with a rating of 80 or above? a) 0 b) 4 c) 96 d) 100 ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: stem-and-leaf display, interpretation 13. Referring to Table 2-4, what percentage of the respondents rated overall television quality with a rating of 50 or below? a) 11 b) 40 c) 44 d) 56 ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: stem-and-leaf display, interpretation 14. Referring to Table 2-4, what percentage of the respondents rated overall television quality with a rating between 50 and 75? a) 11 b) 40 c) 44 d) 56 ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: stem-and-leaf display, interpretation TABLE 2-5 The following are the durations in minutes of a sample of long-distance phone calls made within the continental United States reported by one long-distance carrier. Time (in Minutes) 0 but less than 5 5 but less than 10 10 but less than 15 15 but less than 20 20 but less than 25 25 but less than 30 30 or more

Relative Frequency 0.37 0.22 0.15 0.10 0.07 0.07 0.02

31 Presenting Data in Tables and Charts

15. Referring to Table 2-5, what is the width of each class? a) 1 minute b) 5 minutes c) 2% d) 100% ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: class interval, relative frequency distribution 16. Referring to Table 2-5, if 1,000 calls were randomly sampled, how many calls lasted under 10 minutes? a) 220 b) 370 c) 410 d) 590 ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: relative frequency distribution, interpretation 17. Referring to Table 2-5, if 100 calls were randomly sampled, how many calls lasted 15 minutes or longer? a) 10 b) 14 c) 26 d) 74 ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: relative frequency distribution, interpretation 18. Referring to Table 2-5, if 10 calls lasted 30 minutes or more, how many calls lasted less than 5 minutes? a) 10 b) 185 c) 295 d) 500 ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: relative frequency distribution, interpretation 19. Referring to Table 2-5, what is the cumulative relative frequency for the percentage of calls that lasted under 20 minutes? a) 0.10 b) 0.59 c) 0.76 d) 0.84

Presenting Data in Tables and Charts

ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: cumulative relative frequency 20. Referring to Table 2-5, what is the cumulative relative frequency for the percentage of calls that lasted 10 minutes or more? a) 0.16 b) 0.24 c) 0.41 d) 0.90 ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: cumulative relative frequency

21. Referring to Table 2-5, if 100 calls were randomly sampled,

of them would have lasted

at least 15 minutes but less than 20 minutes a) 0.10 b) 0.16 c) 10 d) 16 ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: relative frequency distribution, interpretation 22. Referring to Table 2-5, if 100 calls were sampled, 15 minutes. a) 26 b) 74 c) 10 d) None of the above.

of them would have lasted less than

ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: relative frequency distribution, interpretation 23. Referring to Table 2-5, if 100 calls were sampled, or more. a) 26 b) 16 c) 74 d) None of the above. ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: relative frequency distribution, interpretation

of them would have lasted 20 minutes

33 Presenting Data in Tables and Charts 24. Referring to Table 2-5, if 100 calls were sampled, minutes or at least 30 minutes or more. a) 35 b) 37 c) 39 d) None of the above.

of them would have lasted less than 5

ANSWER: c TYPE: MC DIFFICULTY: Difficult KEYWORDS: relative frequency distribution, interpretation 25. When studying the simultaneous responses to two categorical questions, we should set up a a) contingency table. b) frequency distribution table. c) cumulative percentage distribution table. d) histogram. ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: contingency table TABLE 2-6 A sample of 200 students at a Big-Ten university was taken after the midterm to ask them whether they went bar hopping the weekend before the midterm or spent the weekend studying, and whether they did well or poorly on the midterm. The following table contains the result.

Studying for Exam Went Bar Hopping

Did Well in Midterm 80 30

Did Poorly in Midterm 20 70

26. Referring to Table 2-6, of those who went bar hopping the weekend before the midterm in the sample, percent of them did well on the midterm. a) 15 b) 27.27 c) 30 d) 55 ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: contingency table, interpretation 27. Referring to Table 2-6, of those who did well on the midterm in the sample, them went bar hopping the weekend before the midterm. a) 15 b) 27.27 c) 30 d) 50 ANSWER: b

percent of

Presenting Data in Tables and Charts

TYPE: MC DIFFICULTY: Easy KEYWORDS: contingency table, interpretation 28. Referring to Table 2-6, percent of the students in the sample went bar hopping the weekend before the midterm and did well on the midterm. a) 15 b) 27.27 c) 30 d) 50 ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: contingency table, interpretation 29. Referring to Table 2-6, percent of the students in the sample spent the weekend studying and did well on the midterm. a) 40 b) 50 c) 72.72 d) 80 ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: contingency table, interpretation 30. Referring to Table 2-6, if the sample is a good representation of the population, we can expect percent of the students in the population to spend the weekend studying and do poorly on the midterm. a) 10 b) 20 c) 45 d) 50 ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: contingency table, interpretation 31. Referring to Table 2-6, if the sample is a good representation of the population, we can expect percent of those who spent the weekend studying to do poorly on the midterm. a) 10 b) 20 c) 45 d) 50 ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: contingency table, interpretation 32. Referring to Table 2-6, if the sample is a good representation of the population, we can expect percent of those who did poorly on the midterm to have spent the weekend studying.

35 Presenting Data in Tables and Charts a) 10 b) 22.22 c) 45 d) 50 ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: contingency table, interpretation 33. In a contingency table, the number of rows and columns a) must always be the same. b) must always be 2. c) must add to 100%. d) None of the above. ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: contingency table 34. Retailers are always interested in determining why a customer selected their store to make a purchase. A sporting goods retailer conducted a customer survey to determine why its customers shopped at the store. The results are shown in the bar chart below. What proportion of the customers responded that they shopped at the store because of the merchandise or the convenience? 20%

Prices

50%

Merchandise

Convenience

15%

Other

15%

10%

20%

30% Responses

40%

50%

60%

a) 35% b) 50% c) 65% d) 85% ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: bar chart, interpretation TABLE 2-7 The Stem-and-Leaf display below contains data on the number of months between the date a civil suit is filed and when the case is actually adjudicated for 50 cases heard in superior court.

Presenting Data in Tables and Charts

Stem 1L 1H 2L 2H 3L 3H 4L 4H 5L 5H 6L 6H

Leaves 23444 7899 222234 55678889 001113 5778 0234 5579 1124 66 15 8

Note: 1L means the “low teens” – 10, 11, 12, 13, or 14; 1H means the “high teens” – 15, 16, 17, 18, or 19; 2L means the “low twenties” – 20, 21, 22, 23, or 24, etc.

35. Referring to Table 2-7, locate the first leaf, i.e., the lowest valued leaf with the lowest valued stem. This represents a wait of

months.

ANSWER: 12 TYPE: FI DIFFICULTY: 1 Easy KEYWORDS: stem-and-leaf display, interpretation 36. Referring to Table 2-7, the civil suit with the longest wait between when the suit was filed and when it was adjudicated had a wait of months. ANSWER: 68 TYPE: FI DIFFICULTY: Easy KEYWORDS: stem-and-leaf display, interpretation 37. Referring to Table 2-7, the civil suit with the fourth shortest waiting time between when the suit was filed and when it was adjudicated had a wait of months. ANSWER: 14 TYPE: FI DIFFICULTY: Moderate KEYWORDS: stem-and-leaf display, interpretation 38. Referring to Table 2-7,

percent of the cases were adjudicated within the first 2 years.

ANSWER: 30 TYPE: FI DIFFICULTY: Moderate KEYWORDS: stem-and-leaf display, interpretation 39. Referring to Table 2-7, years. ANSWER: 20 TYPE: FI DIFFICULTY: Moderate

percent of the cases were not adjudicated within the first 4

37 Presenting Data in Tables and Charts KEYWORDS: stem-and-leaf display, interpretation 40. Referring to Table 2-7, if a frequency distribution with equal sized classes was made from this data, and the first class was "10 but less than 20," the frequency of that class would be ANSWER: 9 TYPE: FI DIFFICULTY: Easy KEYWORDS: stem-and-leaf display, interpretation 41. Referring to Table 2-7, if a frequency distribution with equal sized classes was made from this data, and the first class was "10 but less than 20," the relative frequency of the third class would be . ANSWER: 0.20 or 20% or 10/50 TYPE: FI DIFFICULTY: Moderate KEYWORDS: stem-and-leaf display, relative frequency distribution 42. Referring to Table 2-7, if a frequency distribution with equal sized classes was made from this data, and the first class was "10 but less than 20," the cumulative percentage of the second class would be . ANSWER: 46% or 0.46 or 23/50 TYPE: FI DIFFICULTY: Moderate KEYWORDS: stem-and-leaf display, cumulative percentage distribution TABLE 2-8 The Stem-and-Leaf display represents the number of times in a year that a random sample of 100 "lifetime" members of a health club actually visited the facility. Stem Leaves 0 012222233333344566666667789999 1 1111222234444455669999 2 00011223455556889 3 0000446799 4 011345567 5 0077 6 8 7 67 8 3 9 0247 43. Referring to Table 2-8, the person who has the largest leaf associated with the smallest stem visited the facility times. ANSWER: 9 TYPE: FI DIFFICULTY: Moderate KEYWORDS: stem-and-leaf display, interpretation 44. Referring to Table 2-8, the person who visited the health club less than anyone else in the sample visited the facility times.

Presenting Data in Tables and Charts

ANSWER: 0 or no TYPE: FI DIFFICULTY: Easy KEYWORDS: stem-and-leaf display, interpretation 45. Referring to Table 2-8, the person who visited the health club more than anyone else in the sample visited the facility times. ANSWER: 97 TYPE: FI DIFFICULTY: Easy KEYWORDS: stem-and-leaf display, interpretation 46. Referring to Table 2-8, a year.

of the 100 members visited the health club at least 52 times in

ANSWER: 10 TYPE: FI DIFFICULTY: Moderate KEYWORDS: stem-and-leaf display, interpretation 47. Referring to Table 2-8, times in a year.

of the 100 members visited the health club no more than 12

ANSWER: 38 TYPE: FI DIFFICULTY: Moderate KEYWORDS: stem-and-leaf display, interpretation 48. Referring to Table 2-8, if a frequency distribution with equal sized classes was made from this data, and the first class was "0 but less than 10," the frequency of the fifth class would be . ANSWER: 9 TYPE: FI DIFFICULTY: Moderate KEYWORDS: stem-and-leaf display, frequency distribution 49. Referring to Table 2-8, if a frequency distribution with equal sized classes was made from this data, and the first class was "0 but less than 10," the relative frequency of the last class would be . ANSWER: 4% or 0.04 or 4/100 TYPE: FI DIFFICULTY: Moderate KEYWORDS: stem-and-leaf display, relative frequency distribution 50. Referring to Table 2-8, if a frequency distribution with equal sized classes was made from this data, and the first class was "0 but less than 10," the cumulative percentage of the next-to-last class would be . ANSWER: 96% or 0.96 or 96/100

39 Presenting Data in Tables and Charts TYPE: FI DIFFICULTY: Moderate KEYWORDS: stem-and-leaf display, cumulative percentage distribution 51. Referring to Table 2-8, if a frequency distribution with equal sized classes was made from this data, and the first class was "0 but less than 10," the class midpoint of the third class would be . ANSWER: 25 or (20+30)/2 TYPE: FI DIFFICULTY: Moderate KEYWORDS: stem-and-leaf display, class midpoint TABLE 2-9 The frequency distribution below represents the rents of 250 randomly selected federally subsidized apartments in Minneapolis. Rent in $ Frequency 300 but less than 400 113 400 but less than 500 85 500 but less than 600 32 600 but less than 700 16 700 but less than 800 4 52. Referring to Table 2-9,

apartments rented for at least $400 but less than $600.

ANSWER: 117 TYPE: FI DIFFICULTY: Easy KEYWORDS: frequency distribution

53. Referring to Table 2-9,

percent of the apartments rented for no less than $600.

ANSWER: 8% or 20/250 TYPE: FI DIFFICULTY: Easy KEYWORDS: frequency distribution, cumulative percentage distribution 54. Referring to Table 2-9,

percent of the apartments rented for at least $500.

ANSWER: 20.8% or 52/250 TYPE: FI DIFFICULTY: Moderate KEYWORDS: frequency distribution, cumulative percentage distribution 55. Referring to Table 2-9, the class midpoint of the second class is

ANSWER: 450 TYPE: FI DIFFICULTY: Easy KEYWORDS: frequency distribution, class midpoint 56. Referring to Table 2-9, the relative frequency of the second class is

Presenting Data in Tables and Charts

ANSWER: 85/250 or 17/50 or 34% or 0.34 TYPE: FI DIFFICULTY: Easy KEYWORDS: frequency distribution, relative frequency distribution 57. Referring to Table 2-9, the percentage of apartments renting for less than $600 is

ANSWER: 230/250 or 23/25 or 92% or 0.92 TYPE: FI DIFFICULTY: Moderate KEYWORDS: frequency distribution, cumulative percentage distribution TABLE 2-10 The histogram below represents scores achieved by 200 job applicants on a personality profile. 0.30 Rel.Freq.

0.20

0.10

0.00 0

58. Referring to the histogram from Table 2-10, between 10 and 20.

percent of the job applicants scored

ANSWER: 20% TYPE: FI DIFFICULTY: Easy KEYWORDS: histogram, percentage distribution 59. Referring to the histogram from Table 2-10, 50.

percent of the job applicants scored below

ANSWER: 80% TYPE: FI DIFFICULTY: Moderate KEYWORDS: histogram, percentage distribution

60. Referring to the histogram from Table 2-10, the number of job applicants who scored between 30 and below 60 is

ANSWER: 80 TYPE: FI DIFFICULTY: Moderate

41 Presenting Data in Tables and Charts KEYWORDS: histogram 61. Referring to the histogram from Table 2-10, the number of job applicants who scored 50 or above is . ANSWER: 40 TYPE: FI DIFFICULTY: Moderate KEYWORDS: histogram 62. Referring to the histogram from Table 2-10, 90% of the job applicants scored above or equal to . ANSWER: 10 TYPE: FI DIFFICULTY: Moderate KEYWORDS: histogram, cumulative percentage distribution 63. Referring to the histogram from Table 2-10, half of the job applicants scored below

ANSWER: 30 TYPE: FI DIFFICULTY: Moderate KEYWORDS: histogram, cumulative percentage distribution 64. Referring to the histogram from Table 2-10, or at least 50.

percent of the applicants scored below 20

ANSWER: 50% TYPE: FI DIFFICULTY: Moderate KEYWORDS: histogram, cumulative percentage distribution 65. Referring to the histogram from Table 2-10, 20 and below 50.

percent of the applicants scored between

ANSWER: 50% TYPE: FI DIFFICULTY: Moderate KEYWORDS: histogram, cumulative percentage distribution TABLE 2-11 The ordered array below resulted from taking a sample of 25 batches of 500 computer chips and determining how many in each batch were defective. Defects 1 2 4 17 20 21

4 23

5 23

5 25

6 26

7 27

9 27

9 28

12 29

66. Referring to Table 2-11, if a frequency distribution for the defects data is constructed, using "0 but less than 5" as the first class, the frequency of the “20 but less than 25” class would be .

Presenting Data in Tables and Charts

ANSWER: 4 TYPE: FI DIFFICULTY: Easy KEYWORDS: frequency distribution 67. Referring to Table 2-11, if a frequency distribution for the defects data is constructed, using "0 but less than 5" as the first class, the relative frequency of the “15 but less than 20” class would be . ANSWER: 0.08 or 8% or 2/25 TYPE: FI DIFFICULTY: Moderate KEYWORDS: relative frequency distribution 68. Referring to Table 2-11, construct a frequency distribution for the defects data, using "0 but less than 5" as the first class. ANSWER: Defects Frequency 0 but less than 5 4 5 but less than 10 6 10 but less than 15 2 15 but less than 20 2 20 but less than 25 4 25 but less than 30 7 TYPE: PR DIFFICULTY: Easy KEYWORDS: frequency distribution 69. Referring to Table 2-11, construct a relative frequency or percentage distribution for the defects data, using "0 but less than 5" as the first class. ANSWER: Defects Percentage 0 but less than 5 16 5 but less than 10 24 10 but less than 15 8 15 but less than 20 8 20 but less than 25 16 25 but less than 30 28 TYPE: PR DIFFICULTY: Moderate KEYWORDS: relative frequency distribution, percentage distribution 70. Referring to Table 2-11, construct a cumulative percentage distribution for the defects data if the corresponding frequency distribution uses "0 but less than 5" as the first class. ANSWER: Defects CumPct 0 0 5 16 10 40 15 48 20 56 25 72 30 100

43 Presenting Data in Tables and Charts TYPE: PR DIFFICULTY: Moderate KEYWORDS: cumulative percentage distribution 71. Referring to Table 2-11, construct a histogram for the defects data, using "0 but less than 5" as the first class. ANSWER: 7

Frequency 6

6 5 4

4 3 2

2 1 0

15 20 Number o f Defects

TYPE: PR DIFFICULTY: Easy KEYWORDS: histogram, frequency distribution 72. Referring to Table 2-11, construct a cumulative percentage polygon for the defects data if the corresponding frequency distribution uses "0 but less than 5" as the first class.

ANSWER: Cumulative Percentage Polygon 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% 0

Number of Defects

TYPE: PR DIFFICULTY: Moderate

Presenting Data in Tables and Charts

KEYWORDS: cumulative percentage polygon 73. The point halfway between the boundaries of each class interval in a grouped frequency distribution is called the . ANSWER: class midpoint TYPE: FI DIFFICULTY: Easy KEYWORDS: cumulative percentage polygon, frequency distribution 74. A is a vertical bar chart in which the rectangular bars are constructed at the boundaries of each class interval. ANSWER: histogram TYPE: FI DIFFICULTY: Easy KEYWORDS: histogram 75. It is essential that each class grouping or interval in a frequency distribution be

ANSWER: non-overlapping TYPE: FI DIFFICULTY: Easy KEYWORDS: frequency distribution, class interval 76. In order to compare one large batch of numerical data to another, a be developed from the frequency distribution.

distribution must

ANSWER: relative frequency or percentage TYPE: FI DIFFICULTY: Easy KEYWORDS: relative frequency distribution, percentage distribution 77. When comparing two or more large batches of numerical data, the distributions being developed should use the same . ANSWER: class boundaries. TYPE: FI DIFFICULTY: Easy KEYWORDS: class boundaries 78. It is desirable that the width of each class grouping or interval in a frequency distribution be . ANSWER: the same or equal TYPE: FI DIFFICULTY: Easy KEYWORDS: class interval, frequency distribution 79. In constructing a polygon, each class grouping is represented by its consecutively connected to one another. ANSWER: midpoint

and then these are

45 Presenting Data in Tables and Charts TYPE: FI DIFFICULTY: Easy KEYWORDS: polygon, class interval, midpoint 80. A is a summary table in which numerical data are tallied into class intervals or categories. ANSWER: frequency distribution TYPE: FI DIFFICULTY: Easy KEYWORDS: frequency distribution, class interval 81. True or False: In general, grouped frequency distributions should have between 5 and 15 class intervals. ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: frequency distribution, number of classes 82. True or False: The sum of relative frequencies in a distribution always equals 1. ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: relative frequency 83. True or False: The sum of cumulative frequencies in a distribution always equals 1. ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: cumulative frequency distribution 84. True or False: In graphing bivariate categorical data, the side-by-side bar chart is best suited when primary interest is in demonstrating differences in magnitude rather than differences in percentages. ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: side-by-side chart 85. True or False: When constructing a frequency distribution, classes should be selected in such a way that they are of equal width. ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: frequency distribution 86. True or False: A research analyst was directed to arrange raw data collected on the yield of wheat, ranging from 40 to 93 bushels per acre, in a frequency distribution. He should choose 30 as the class interval width.

Presenting Data in Tables and Charts

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: frequency distribution, class interval 87. True or False: If the values of the seventh and eighth class in a cumulative frequency distribution are the same, we know that there are no observations in the eighth class. ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: cumulative frequency distribution

88. True or False: Research on Human perception concludes that the bar chart is preferred to the pie chart, because the human eye can more accurately judge length comparisons against a fixed scale (as in a bar chart) than angular measures (as in a pie chart). ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: bar chart, pie chart 89. True or False: One of the advantages of a pie chart is that it clearly shows that the total of all the categories of the pie adds to 100%. ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: pie chart 90. True or False: The larger the number of observations in a numerical data set, the larger the number of class intervals needed for a grouped frequency distribution. ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: class interval, frequency distribution 91. True or False: Determining the class boundaries of a frequency distribution is highly subjective. ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: class boundaries, frequency distribution 92. True or False: The original data values cannot be assessed once they are grouped into a frequency distribution table. ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: frequency distribution

47 Presenting Data in Tables and Charts 93. True or False: The percentage distribution cannot be constructed from the frequency distribution directly. ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: percentage distribution, frequency distribution 94. True or False: The stem-and-leaf display is often superior to the frequency distribution in that it maintains the original values for further analysis. ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: stem-and-leaf display, frequency distribution 95. True or False: The relative frequency is the frequency in each class divided by the total number of observations. ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: relative frequency distribution 96. True or False: Ogives are plotted at the midpoints of the class groupings. ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: ogives, midpoint 97. True or False: Percentage polygons are plotted at the boundaries of the class groupings. ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: percentage polygons 98. True or False: The main principle behind the Pareto diagram is the ability to track the "vital few" from the "trivial many." ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: Pareto diagram 99. True or False: A histogram can have gaps between the bars, whereas bar charts cannot have gaps. ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: histogram, bar chart

Presenting Data in Tables and Charts

100. True or False: Histograms are used for numerical data while bar charts are suitable for categorical data. ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: histogram, bar chart

101. True or False: A Wal-Mart store in a small town monitors customer complaints and organizes these complaints into six distinct categories. Over the past year, the company has received 534 complaints. One possible graphical method for representing these data would be a Pareto chart. ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: Pareto diagram 102. True or False: Apple Computer, Inc. collected information on the age of their customers. The youngest customer was 12 and the oldest was 72. To study the distribution of the age among its customers, it can use a Pareto diagram. ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: Pareto diagram

103. True or False: Apple Computer, Inc. collected information on the age of their customers. The youngest customer was 12 and the oldest was 72. To study the distribution of the age among its customers, it is best to use a pie chart. ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: pie chart 104. True or False: Apple Computer, Inc. collected information on the age of their customers. The youngest customer was 12 and the oldest was 72. To study the distribution of the age among its customers, it can use a percentage polygon. ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: percentage polygon 105. True or False: Apple Computer, Inc. collected information on the age of their customers. The youngest customer was 12 and the oldest was 72. To study the percentage of their customers who are below a certain age, it can use an ogive. ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: ogive

49 Presenting Data in Tables and Charts 106. True or False: If you wish to construct a graph of a relative frequency distribution, you would most likely construct an ogive first. ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: ogive 107.

True or False: An ogive is a cumulative percentage polygon.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: ogive, cumulative percentage polygon

108. True or False: A side-by-side chart is two histograms plotted side-by-side. ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: side-by-side chart

109. True or False: A good choice for the number of class groups to use in constructing frequency distribution is to have at least 5 but no more than 15 class groups. ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: number of classes 110. True or False: In general, a frequency distribution should have at least 8 class groups but no more than 20. ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: number of classes 111. True of False: To determine the width of class interval, divide the number of class groups by the range of the data. ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: class interval 112. True or False: The percentage polygon is formed by having the lower boundary of each class represent the data in that class and then connecting the sequence of lower boundaries at their respective class percentages. ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: percentage polygon

Presenting Data in Tables and Charts

113.

True or False: A polygon can be constructed from a bar chart.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: polygon

114. To evaluate two categorical variables at the same time, a

could be developed.

ANSWER: contingency or cross-classification table or side-by-side bar chart TYPE: FI DIFFICULTY: Easy KEYWORDS: contingency table, cross-classification table 115. Relationships in a contingency table can be examined more fully if the frequencies are converted into . ANSWER: percentages or proportions TYPE: FI DIFFICULTY: Easy KEYWORDS: contingency table TABLE 2-12 The table below contains the opinions of a sample of 200 people broken down by gender about the latest congressional plan to eliminate anti-trust exemptions for professional baseball. Female Male Totals 116.

For 38 12 50

Neutral 54 36 90

Against Totals 12 104 48 96 60 200

Referring to Table 2-12, construct a table of row percentages.

ANSWER: For Neutral Against Female 36.54 51.92 11.54 Male 12.50 37.50 50.00 Totals 25.00 45.00 30.00 TYPE: PR DIFFICULTY: Easy KEYWORDS: row percentages 117.

Totals 100.00 100.00 100.00

Referring to Table 2-12, construct a table of column percentages.

ANSWER: For Neutral Against Totals Female 76.00 60.00 20.00 52.00 Male 24.00 40.00 80.00 48.00 Totals 100.00 100.00 100.00 100.00 TYPE: PR DIFFICULTY: Easy KEYWORDS: column percentages 118.

Referring to Table 2-12, construct a table of total percentages.

51 Presenting Data in Tables and Charts

ANSWER: For Neutral Against Totals Female 19.00 27.00 6.00 52.00 Male 6.00 18.00 24.00 48.00 Totals 25.00 45.00 30.00 100.00 TYPE: PR DIFFICULTY: Easy KEYWORDS: total percentages 119.

Referring to Table 2-12, of those for the plan in the sample,

percent were females.

ANSWER: 76% TYPE: FI DIFFICULTY: Moderate KEYWORDS: contingency table, column percentages 120.

Referring to Table 2-12, of those neutral in the sample,

percent were males.

ANSWER: 40% TYPE: FI DIFFICULTY: Moderate KEYWORDS: contingency table, column percentages 121.

Referring to Table 2-12, of the males in the sample,

percent were for the plan.

ANSWER: 12.50% TYPE: FI DIFFICULTY: Moderate KEYWORDS: contingency table 122.

Referring to Table 2-12, of the females in the sample,

percent were against the plan.

ANSWER: 11.54% TYPE: FI DIFFICULTY: Moderate KEYWORDS: contingency table 123. Referring to Table 2-12, of the females in the sample, against the plan.

percent were either neutral or

ANSWER: 63.46% or (51.92+11.54)% TYPE: FI DIFFICULTY: Moderate KEYWORDS: contingency table 124.

Referring to Table 2-12,

percent of the 200 were females who were against the plan.

ANSWER: 6% TYPE: FI DIFFICULTY: Moderate KEYWORDS: contingency table 125.

Referring to Table 2-12,

percent of the 200 were males who were neutral.

Presenting Data in Tables and Charts

ANSWER: 18% TYPE: FI DIFFICULTY: Moderate KEYWORDS: contingency table 126. Referring to Table 2-12, against the plan.

percent of the 200 were females who were either neutral or

ANSWER: 33% TYPE: FI DIFFICULTY: Difficult KEYWORDS: contingency table 127.

Referring to Table 2-12,

percent of the 200 were males who were not against the plan.

ANSWER: 24% TYPE: FI DIFFICULTY: Difficult KEYWORDS: contingency table 128.

Referring to Table 2-12,

percent of the 200 were not neutral.

ANSWER: 55% TYPE: FI DIFFICULTY: Difficult KEYWORDS: contingency table, row percentages 129.

Referring to Table 2-12,

percent of the 200 were against the plan.

ANSWER: 30% TYPE: FI DIFFICULTY: Moderate KEYWORDS: contingency table, row percentages 130.

Referring to Table 2-12,

percent of the 200 were males.

ANSWER: 48% TYPE: FI DIFFICULTY: Easy KEYWORDS: contingency table, column percentages 131.

Referring to Table 2-12, if the sample is a good representation of the population, we can expect percent of the population will be for the plant.

ANSWER: 25% TYPE: FI DIFFICULTY: Moderate KEYWORDS: contingency table, row percentages 132.

Referring to Table 2-12, if the sample is a good representation of the population, we can expect percent of the population will be males.

ANSWER: 48%

53 Presenting Data in Tables and Charts TYPE: FI DIFFICULTY: Moderate KEYWORDS: contingency table, column percentages 133.

Referring to Table 2-12, if the sample is a good representation of the population, we can expect percent of those for the plan in the population will be males.

ANSWER: 24% TYPE: FI DIFFICULTY: Moderate KEYWORDS: contingency table 134.

Referring to Table 2-12, if the sample is a good representation of the population, we can expect percent of the males in the population will be against the plan.

ANSWER: 50% TYPE: FI DIFFICULTY: Moderate KEYWORDS: contingency table 135.

Referring to Table 2-12, if the sample is a good representation of the population, we can expect percent of the females in the population will not be against the plan.

ANSWER: 88.46% or (36.54+51.92) TYPE: FI DIFFICULTY: Moderate KEYWORDS: contingency table TABLE 2-13 Given below is the stem-and-leaf display representing the amount of detergent used in gallons (with leaves in 10ths of gallons) in a month by 25 drive-through car wash operations in Phoenix. 9 | 147 10 | 02238 11 | 135566777 12 | 223489 13 | 02

136. Referring to Table 2-13, if a frequency distribution for the amount of detergent used is

constructed, using "9.0 but less than 10.0 gallons" as the first class, the frequency of the “11.0 but less than 12.0 gallons” class would be .

ANSWER: 9 TYPE: FI DIFFICULTY: Easy KEYWORDS: frequency distribution

137. Referring to Table 2-13, if a percentage histogram for the detergent data is constructed, using "9.0 but less than 10.0 gallons" as the first class, the percentage of drive-through car wash operations that use “12.0 but less than 13.0 gallons” of detergent would be . ANSWER: 24% TYPE: FI DIFFICULTY: Moderate

Presenting Data in Tables and Charts

KEYWORDS: relative frequency distribution, percentage distribution

138. Referring to Table 2-13, if a percentage histogram for the detergent data is constructed, using "9.0 but less than 10.0 gallons" as the first class, what percentage of drive-through car wash operations use less than 12 gallons of detergent in a month? ANSWER: 68% TYPE: FI DIFFICULTY: Easy KEYWORDS: percentage distribution, cumulative relative frequency

139. Referring to Table 2-13, if a relative frequency or percentage distribution for the detergent data is constructed, using "9.0 but less than 10.0 gallons" as the first class, what percentage of drivethrough car wash operations use at least 10 gallons of detergent in a month? ANSWER: 88% TYPE: FI DIFFICULTY: Easy KEYWORDS: relative frequency distribution, percentage distribution

140. Referring to Table 2-13, if a relative frequency or percentage distribution for the detergent data is constructed, using "9.0 but less than 10.0 gallons" as the first class, what percentage of drivethrough car wash operations use at least 10 gallons but less than 13 gallons of detergent in a month? ANSWER: 80% TYPE: FI DIFFICULTY: Easy KEYWORDS: relative frequency distribution, percentage distribution

141. Referring to Table 2-13, construct a frequency distribution for the detergent data, using "9.0 but less than 10.0 gallons" as the first class. ANSWER: Purchases (gals) Frequency 9.0 but less than 10.0 3 10.0 but less than 11.0 5 11.0 but less than 12.0 9 12.0 but less than 13.0 6 13.0 but less than 14.0 2 TYPE: PR DIFFICULTY: Moderate KEYWORDS: frequency distribution

142. Referring to Table 2-13, construct a relative frequency or percentage distribution for the detergent data, using "9.0 but less than 10.0" as the first class. ANSWER: Gasoline Purchases (gals) 9.0 but less than 10.0 10.0 but less than 11.0 11.0 but less than 12.0 12.0 but less than 13.0

Percentage 12% 20 36 24

55 Presenting Data in Tables and Charts 13.0 but less than 14.0 8 TYPE: PR DIFFICULTY: Moderate KEYWORDS: relative frequency distribution, percentage distribution

143. Referring to Table 2-13, construct a cumulative percentage distribution for the detergent data if the corresponding frequency distribution uses "9.0 but less than 10.0" as the first class. ANSWER: Gasoline Frequency Percentage Purchases (gals) Less Than Less Than 9.0 but less than 10.0 3 12 10.0 but less than 11.0 8 32 11.0 but less than 12.0 17 68 12.0 but less than 13.0 23 92 13.0 but less than 14.0 25 100 TYPE: PR DIFFICULTY: Moderate KEYWORDS: cumulative percentage distribution

144. Referring to Table 2-13, construct a percentage histogram for the detergent data, using "9.0 but less than 10.0" as the first class. ANSWER: % Histogram 40 35 30

25 20 15 10 5 0 9.0 -- 9.9

10.0 -- 10.9 11.0 -- 11.9 12.0 -- 12.9 13.0 -- 13.9 Purchased

TYPE: PR DIFFICULTY: Moderate KEYWORDS: histogram, frequency distribution

145. Referring to Table 2-13, construct a cumulative percentage polygon for the detergent data if the corresponding frequency distribution uses "9.0 but less than 10.0" as the first class.

ANSWER:

Presenting Data in Tables and Charts

Ogive 100 80

60 40 20 0 9

Purchase

TYPE: PR DIFFICULTY: Moderate KEYWORDS: cumulative percentage polygon

146. Referring to Table 2-13, construct a percentage polygon for the detergent data if the corresponding frequency distribution uses "9.0 but less than 10.0" as the first class.

ANSWER:

% Polygon 40 35 30 25 20 15 10 5 0

8.5

9.5

10.5

11.5

12.5

13.5

14.5

Purchase

TYPE: PR DIFFICULTY: Moderate KEYWORDS: percentage distribution TABLE 2-14 The table below contains the number of people who own a portable DVD player in a sample of 600 broken down by gender. Own a Portable DVD Player Yes No 147.

Male 96 224

Female 40 240

Referring to Table 2-14, construct a table of row percentages.

ANSWER: Own Yes

Male 70.59%

Female 29.41%

Total 100.00%

57 Presenting Data in Tables and Charts No Total

48.28% 53.33%

51.72% 46.67%

100.00% 100.00%

TYPE: PR DIFFICULTY: Easy KEYWORDS: row percentages

148. Referring to Table 2-14, construct a table of column percentages. ANSWER: Own Yes No Total

Male 30.00% 70.00% 100.00%

Female 14.29% 85.71% 100.00%

Total 22.67% 77.33% 100.00%

TYPE: PR DIFFICULTY: Easy KEYWORDS: column percentages

149. Referring to Table 2-14, construct a table of total percentages. ANSWER: Own Yes No Total

Male 16.00% 37.33% 53.33%

Female 6.67% 40.00% 46.67%

Total 22.67% 77.33% 100.00%

TYPE: PR DIFFICULTY: Easy KEYWORDS: total percentages

150. Referring to Table 2-14, of those who owned a portable DVD in the sample,

percent

were females. ANSWER: 29.41% TYPE: FI DIFFICULTY: Moderate KEYWORDS: contingency table, row percentages

151. Referring to Table 2-14, of those who did not own a portable DVD in the sample, percent were males. ANSWER: 48.28% TYPE: FI DIFFICULTY: Moderate KEYWORDS: contingency table, row percentages

152. Referring to Table 2-14, of the males in the sample,

percent owned a portable DVD.

ANSWER: 30% TYPE: FI DIFFICULTY: Moderate KEYWORDS: contingency table, column percentages

153. Referring to Table 2-14, of the females in the sample, DVD. ANSWER:

percent did not own a portable

Presenting Data in Tables and Charts

85.71% TYPE: FI DIFFICULTY: Moderate KEYWORDS: contingency table, column percentages

154. Referring to Table 2-14, of the females in the sample,

percent owned a portable

DVD. ANSWER: 14.29% TYPE: FI DIFFICULTY: Moderate KEYWORDS: contingency table, column percentages

155. Referring to Table 2-14,

percent of the 600 were females who owned a portable

DVD. ANSWER: 6.67% TYPE: FI DIFFICULTY: Moderate KEYWORDS: contingency table, total percentage

156. Referring to Table 2-14,

percent of the 600 were males who owned a portable DVD.

ANSWER: 16% TYPE: FI DIFFICULTY: Moderate KEYWORDS: contingency table, total percentage

157. Referring to Table 2-14,

percent of the 600 were females who either owned or did

not own a portable DVD. ANSWER: 46.67% TYPE: FI DIFFICULTY: Moderate KEYWORDS: contingency table, total percentage

158. Referring to Table 2-14,

percent of the 600 were males who did not owned a portable

DVD. ANSWER: 37.33% TYPE: FI DIFFICULTY: Moderate KEYWORDS: contingency table, total percentage

159. Referring to Table 2-14,

percent of the 600 owned a portable DVD.

ANSWER: 22.67% TYPE: FI DIFFICULTY: Moderate KEYWORDS: contingency table, column percentages

160. Referring to Table 2-14, ANSWER:

percent of the 600 did not owned a portable DVD.

59 Presenting Data in Tables and Charts 77.33% TYPE: FI DIFFICULTY: Moderate KEYWORDS: contingency table, column percentages

161. Referring to Table 2-14,

percent of the 600 were females.

ANSWER: 46.67% TYPE: FI DIFFICULTY: Easy KEYWORDS: contingency table, row percentages

162. Referring to Table 2-14, if the sample is a good representation of the population, we can expect percent of the population will own a portable DVD. ANSWER: 22.67% TYPE: FI DIFFICULTY: Moderate KEYWORDS: contingency table, column percentages

163. Referring to Table 2-14, if the sample is a good representation of the population, we can expect percent of the population will be males. ANSWER: 53.33% TYPE: FI DIFFICULTY: Moderate KEYWORDS: contingency table, column percentages

164. Referring to Table 2-14, if the sample is a good representation of the population, we can expect percent of those who own a portable DVD in the population will be males. ANSWER: 70.59% TYPE: FI DIFFICULTY: Moderate KEYWORDS: contingency table, row percentages

165. Referring to Table 2-14, if the sample is a good representation of the population, we can expect percent of the males in the population will own a portable DVD. ANSWER: 30% TYPE: FI DIFFICULTY: Moderate KEYWORDS: contingency table, column percentages

166. Referring to Table 2-14, if the sample is a good representation of the population, we can expect percent of the females in the population will not own a portable DVD. ANSWER: 85.71% TYPE: FI DIFFICULTY: Moderate KEYWORDS: contingency table, column percentages

Numerical Descriptive Measures

CHAPTER 3: NUMERICAL DESCRIPTIVE MEASURES 1. Which of the following statistics is not a measure of central tendency? a) arithmetic mean b) median c) mode d) Q3 ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: measure of central tendency, arithmetic mean, median, mode, quartiles 2. Which measure of central tendency can be used for both numerical and categorical variables? a) arithmetic mean b) median c) mode d) geometric mean ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: measure of central tendency, mode, arithmetic mean, median, geometric mean 3. Which of the arithmetic mean, median, mode, and geometric mean are resistant measures of central tendency? a) the arithmetic mean and median only b) the median and mode only c) the mode and geometric mean only d) the arithmetic mean and mode only ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: measure of central tendency, resistant to outliers, mean, median, mode 4. In a right-skewed distribution a) the median equals the arithmetic mean. b) the median is less than the arithmetic mean. c) the median is larger than the arithmetic mean. d) None of the above. ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: shape 5. Which of the following statements about the median is not true? a) It is more affected by extreme values than the arithmetic mean. b) It is a measure of central tendency. c) It is equal to Q2. d) It is equal to the mode in bell-shaped "normal" distributions.

66 Numerical Descriptive Measures

ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: median, measure of central tendency, resistant to outliers, quartile 6. In a perfectly symmetrical bell-shaped "normal" distribution a) the arithmetic mean equals the median. b) the median equals the mode. c) the arithmetic mean equals the mode. d) All the above. ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: shape, normal distribution 7. In a perfectly symmetrical distribution a) the range equals the interquartile range. b) the interquartile range equals the arithmetic mean. c) the median equals the arithmetic mean. d) the variance equals the standard deviation. ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: shape

8. When extreme values are present in a set of data, which of the following descriptive summary measures are most appropriate? a) CV and range b) arithmetic mean and standard deviation c) interquartile range and median d) variance and interquartile range ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: resistant to outliers, coefficient of variation, range, arithmetic mean, standard deviation, interquartile range, median, variance 9. In general, which of the following descriptive summary measures cannot be easily approximated from a box-and-whisker plot? a) the variance b) the range c) the interquartile range d) the median ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: box-and-whisker plot, variance, range, interquartile range, median 10. The smaller the spread of scores around the arithmetic mean,

Numerical Descriptive Measures a) b) c) d)

the smaller the interquartile range. the smaller the standard deviation. the smaller the coefficient of variation. All the above.

ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: variation, arithmetic mean, interquartile range, standard deviation, coefficient of variation 11. Which descriptive summary measures are considered to be resistant statistics? a) the arithmetic mean and standard deviation b) the interquartile range and range c) the mode and variance d) the median and interquartile range ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: resistant to outliers, arithmetic mean, standard deviation, interquartile range, range, mode, variance, median 12. In right-skewed distributions, which of the following is the correct statement? a) The distance from Q1 to Q2 is larger than the distance from Q2 to Q3. b) The distance from Q1 to Q2 is smaller than the distance from Q2 to Q3. c) The arithmetic mean is smaller than the median. d) The mode is larger than the arithmetic mean. ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: shape, quartiles, arithmetic mean, mode 13. In perfectly symmetrical distributions, which of the following is NOT a correct statement? a) The distance from Q1 to Q2 equals to the distance from Q2 to Q3. b) The distance from the smallest observation to Q1 is the same as the distance from Q3 to the largest observation. c) The distance from the smallest observation to Q2 is the same as the distance from Q2 to the largest observation. d) The distance from Q1 to Q3 is half of the distance from the smallest to the largest observation. ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: shape, quartiles, five-number summary, quartiles 14. In left-skewed distributions, which of the following is the correct statement? a) The distance from Q1 to Q2 is smaller than the distance from Q2 to Q3. b) The distance from the smallest observation to Q1 is larger than the distance from Q3 to the largest observation.

68 Numerical Descriptive Measures c) The distance from the smallest observation to Q2 is smaller than the distance from Q2 to the largest observation. d) The distance from Q1 to Q3 is twice the distance from the Q1 to Q2. ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: shape, quartiles, five-number summary, quartiles 15. According to the empirical rule, if the data form a "bell-shaped" normal distribution, percent of the observations will be contained within 2 standard deviations around the arithmetic mean. a) 68.26 b) 88.89 c) 93.75 d) 95.44 ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: empirical rule, normal distribution 16. According to the empirical rule, if the data form a "bell-shaped" normal distribution, percent of the observations will be contained within 1 standard deviation around the arithmetic mean. a) 68.26 b) 75.00 c) 88.89 d) 93.75 ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: empirical rule, normal distribution 17. According to the empirical rule, if the data form a "bell-shaped" normal distribution, percent of the observations will be contained within 3 standard deviations around the arithmetic mean. a) 68.26 b) 75.00 c) 95.0 d) 99.7 ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: empirical rule, normal distribution 18. Which of the following is NOT a measure of central tendency? a) the arithmetic mean b) the geometric mean c) the mode d) the interquartile range

Numerical Descriptive Measures

ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: measure of central tendency, arithmetic mean, geometric mean, mode, interquartile range 19. Which of the following is NOT sensitive to extreme values? a) the range b) the standard deviation c) the interquartile range d) the coefficient of variation ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: resistant to outliers, range, standard deviation, interquartile range, coefficient of variation 20. Which of the following is sensitive to extreme values? a) the median b) the interquartile range c) the arithmetic mean d) the 1st quartile ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: resistant to outliers, median, interquartile range, arithmetic mean, quartiles 21. Which of the following is the easiest to compute? a) the arithmetic mean b) the median c) the mode d) the geometric mean ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: mode, arithmetic mean, median, geometric mean 22. According to the Chebyshev rule, at least 75% of all observations in any data set are contained within a distance of how many standard deviations around the mean? a) 1 b) 2 c) 3 d) 4 ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: Chebyshev rule

70 Numerical Descriptive Measures 23. According to the Chebyshev rule, at least 93.75% of all observations in any data set are contained within a distance of how many standard deviations around the mean? a) 1 b) 2 c) 3 d) 4 ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: Chebyshev rule 24. According to the Chebyshev rule, at least what percentage of the observations in any data set are contained within a distance of 3 standard deviations around the mean? a) 67% b) 75% c) 88.89% d) 99.7% ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: Chebyshev rule 25. According to the Chebyshev rule, at least what percentage of the observations in any data set are contained within a distance of 2 standard deviations around the mean? a) 67% b) 75% c) 88.89% d) 95% ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: Chebyshev rule TABLE 3-1 Health care issues are receiving much attention in both academic and political arenas. A sociologist recently conducted a survey of citizens over 60 years of age whose net worth is too high to qualify for Medicaid and have no private health insurance. The ages of 25 uninsured senior citizens were as follows: 60 61 62 63 64 65 66 68 68 69 70 73 73 74 75 76 76 81 81 82 86 87 89 90 92 26. Referring to Table 3-1, calculate the arithmetic mean age of the uninsured senior citizens to the nearest hundredth of a year. ANSWER: 74.04 years TYPE: PR DIFFICULTY: Easy KEYWORDS: arithmetic mean 27. Referring to Table 3-1, identify the median age of the uninsured senior citizens.

Numerical Descriptive Measures

ANSWER: 73 years TYPE: PR DIFFICULTY: Easy KEYWORDS: median 28. Referring to Table 3-1, identify the first quartile of the ages of the uninsured senior citizens. ANSWER: 65.5 years TYPE: PR DIFFICULTY: Moderate KEYWORDS: quartiles 29. Referring to Table 3-1, identify the third quartile of the ages of the uninsured senior citizens. ANSWER: 81.5 years TYPE: PR DIFFICULTY: Moderate KEYWORDS: quartiles 30. Referring to Table 3-1, identify the interquartile range of the ages of the uninsured senior citizens. ANSWER: 16 years TYPE: PR DIFFICULTY: Moderate KEYWORDS: interquartile range 31. Referring to Table 3-1, identify which of the following is the correct statement. a) One fourth of the senior citizens sampled are below 65.5 years of age. b) The middle 50% of the senior citizens sampled are between 65.5 and 73.0 years of age. c) The average age of senior citizens sampled is 73.5 years of age. d) All of the above are correct. ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: quartiles, arithmetic mean 32. Referring to Table 3-1, identify which of the following is the correct statement. a) One fourth of the senior citizens sampled are below 64 years of age. b) The middle 50% of the senior citizens sampled are between 65.5 and 73.0 years of age. c) 25% of the senior citizens sampled are older than 81.5 years of age. d) All of the above are correct. ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: quartiles 33. Referring to Table 3-1, what type of shape does the distribution of the sample appear to have? ANSWER: Slightly positive or right-skewed. TYPE: PR DIFFICULTY: Moderate

72 Numerical Descriptive Measures KEYWORDS: shape 34. Referring to Table 3-1, calculate the variance of the ages of the uninsured senior citizens correct to the nearest hundredth of a year squared. ANSWER: 94.96 years2 TYPE: PR DIFFICULTY: Moderate KEYWORDS: variance 35. Referring to Table 3-1, calculate the standard deviation of the ages of the uninsured senior citizens correct to the nearest hundredth of a year. ANSWER: 9.74 years TYPE: PR DIFFICULTY: Moderate KEYWORDS: standard deviation 36. Referring to Table 3-1, calculate the coefficient of variation of the ages of the uninsured senior citizens. ANSWER: 13.16% TYPE: PR DIFFICULTY: Moderate KEYWORDS: coefficient of variation 37. True or False: The median of the values 3.4, 4.7, 1.9, 7.6, and 6.5 is 1.9. ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: median 38. True or False: The median of the values 3.4, 4.7, 1.9, 7.6, and 6.5 is 4.05. ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: median 39. True or False: In a set of numerical data, the value for Q3 can never be smaller than the value for Q1. ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: quartiles 40. True or False: In a set of numerical data, the value for Q2 is always halfway between Q1 and Q3. ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: quartiles

Numerical Descriptive Measures

41. True or False: If the distribution of a data set were perfectly symmetrical, the distance from Q1 to the median would always equal the distance from Q3 to the median in a box-and-whisker plot. ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: box-and-whisker plot, quartiles, shape 42. True or False: In right-skewed distributions, the distance from Q3 to the largest observation exceeds the distance from the smallest observation to Q1. ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: quartiles, shape 43. True or False: In left-skewed distributions, the distance from the smallest observation to Q1 exceeds the distance from Q3 to the largest observation. ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: quartiles, shape 44. True or False: A box-and-whisker plot is a graphical representation of a 5-number summary. ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: box-and-whisker plot, five-number summary 45. True or False: The 5-number summary consists of the smallest observation, the first quartile, the median, the third quartile, and the largest observation. ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: five-number summary 46. True or False: In a box-and-whisker plot, the box portion represents the data between the first and third quartile values. ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: box-and-whisker plot 47. True or False: The line drawn within the box of the box-and-whisker plot always represents the arithmetic mean. ANSWER: False TYPE: TF DIFFICULTY: Easy

74 Numerical Descriptive Measures KEYWORDS: box-and-whisker plot, arithmetic mean 48. True or False: The line drawn within the box of the box-and-whisker plot always represents the median. ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: box-and-whisker plot, median

49. True or False: In a sample of size 40, the sample mean is 15. In this case, the sum of all observations in the sample is  Xi = 600. ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: arithmetic mean 50. True or False: A population with 200 elements has an arithmetic mean of 10. From this information, it can be shown that the population standard deviation is 15. ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: arithmetic mean, standard deviation 51. True or False: In exploratory data analysis, a box-and-whisker plot can be used to illustrate the median, quartiles, and extreme values. ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: box-and-whisker plot, five-number summary 52. True or False: An economics professor bases his final grade on homework, two midterm examinations, and a final examination. The homework counts 10% toward the final grade, while each midterm examination counts 25%. The remaining portion consists of the final examination. If a student scored 95% in homework, 70% on the first midterm examination, 96% on the second midterm examination, and 72% on the final, his final average is 79.8%. ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: arithmetic mean 53. True or False: The median of a data set with 20 items would be the average of the 10th and the 11th items in the ordered array. ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: median, arithmetic mean

Numerical Descriptive Measures

54. True or False: The coefficient of variation measures variability in a data set relative to the size of the arithmetic mean. ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: coefficient of variation 55. True or False: The coefficient of variation is expressed as a percentage. ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: coefficient of variation 56. True or False: The coefficient of variation is a measure of central tendency in the data. ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: coefficient of variation, measure of variation 57. True or False: The interquartile range is a measure of variation or dispersion in a set of data. ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: interquartile range, measure of variation 58. True or False: The interquartile range is a measure of central tendency in a set of data. ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: interquartile range, measure of variation 59. True or False: The geometric mean is a measure of variation or dispersion in a set of data. ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: geometric mean, measure of central tendency 60. True or False: The geometric mean is useful in measuring the rate of change of a variable over time. ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: geometric mean 61. True or False: If a set of data is perfectly symmetrical, the arithmetic mean must be identical to the median.

76 Numerical Descriptive Measures ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: shape, arithmetic mean, median 62. True or False: The coefficient of variation is a measure of relative variation. ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: coefficient of variation 63. True or False: If the data set is approximately bell-shaped, the empirical rule will more accurately reflect the greater concentration of data close to the mean as compared to the Chebyshev rule. ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: empirical rule, Chebyshev rule, normal distribution 64. If the arithmetic mean of a numerical data set exceeds the median, the data are considered to be skewed. ANSWER: positive or right TYPE: FI DIFFICULTY: Easy KEYWORDS: shape, arithmetic mean, median TABLE 3-2 The data below represent the amount of grams of carbohydrates in a serving of breakfast cereal in a sample of 11 different servings. 11 15 23 29 19 22 21 20 15 25 17 65. Referring to Table 3-2, the arithmetic mean carbohydrates in this sample is

grams.

ANSWER: 217/11 = 19.73 TYPE: FI DIFFICULTY: Moderate KEYWORDS: arithmetic mean 66. Referring to Table 3-2, the median carbohydrate amount in the cereal is

grams.

ANSWER: 20 TYPE: FI DIFFICULTY: Moderate KEYWORDS: median 67. Referring to Table 3-2, the first quartile of the carbohydrate amounts is ANSWER: 15 TYPE: FI DIFFICULTY: Moderate KEYWORDS: quartiles

grams.

Numerical Descriptive Measures 68. Referring to Table 3-2, the third quartile of the carbohydrate amounts is

grams.

ANSWER: 23 TYPE: FI DIFFICULTY: Moderate KEYWORDS: quartiles 69. Referring to Table 3-2, the range in the carbohydrate amounts is

grams.

ANSWER: 18 TYPE: FI DIFFICULTY: Easy KEYWORDS: range 70. Referring to Table 3-2, the interquartile range in the carbohydrate amounts is

grams.

ANSWER: 8 TYPE: FI DIFFICULTY: Moderate KEYWORDS: interquartile range 71. Referring to Table 3-2, the variance of the carbohydrate amounts is

(grams squared).

ANSWER: 26.02 TYPE: FI DIFFICULTY: Moderate KEYWORDS: variance 72. Referring to Table 3-2, the standard deviation of the carbohydrate amounts is

grams.

ANSWER: 5.10 TYPE: FI DIFFICULTY: Moderate KEYWORDS: standard deviation 73. Referring to Table 3-2, the coefficient of variation of the carbohydrate amounts is percent. ANSWER: 25.86% TYPE: FI DIFFICULTY: Moderate KEYWORDS: coefficient of variation 74. Referring to Table 3-2, the five-number summary of the carbohydrate amounts consists of , , , , . ANSWER: 11, 15, 20, 23, 29 TYPE: FI DIFFICULTY: Moderate KEYWORDS: five-number summary 75. Referring to Table 3-2, construct a box-and-whisker plot for the carbohydrate amounts.

78 Numerical Descriptive Measures ANSWER: Box-and-whisker Plot

TYPE: PR DIFFICULTY: Moderate KEYWORDS: box-and-whisker plot 76. Referring to Table 3-2, what type of shape does the distribution of the sample appear to have? ANSWER: Slightly positive or right-skewed. TYPE: PR DIFFICULTY: Moderate EXPLANATION: The distribution is considered as slightly right-skewed because the length of the right whisker (6) is slighter longer than the length of the left whisker (4). The distribution could also be considered as slight left-skewed since the mean (19.73) is slightly lower than the median (20). KEYWORDS: shape TABLE 3-3 The stem-and-leaf display below represents the number of vitamin supplements sold by a health food store in a sample of 16 days. Stem Leaves 1H 99 2L 0023 2H 567 3L 034 3H 568 4L 1 Note (1): 1H means the “high teens” – 15, 16, 17, 18, or 19; 2L means the “low twenties” – 20, 21, 22, 23, or 24; 2H means the “high twenties” – 25, 26, 27, 28, or 29, etc. Note (2): For this sample, the sum of the observations is 448, the sum of the squares of the observations is 13,356, and the sum of the squared differences between each observation and the mean is 812. 77. Referring to Table 3-3, the arithmetic mean of the number of vitamin supplements sold in this sample is . ANSWER: 28 TYPE: FI DIFFICULTY: Easy KEYWORDS: arithmetic mean

Numerical Descriptive Measures

78. Referring to Table 3-3, the first quartile of the number of vitamin supplements sold in this sample is . ANSWER: 20 TYPE: FI DIFFICULTY: Moderate KEYWORDS: quartiles 79. Referring to Table 3-3, the third quartile of the number of vitamin supplements sold in this sample is . ANSWER: 35 TYPE: FI DIFFICULTY: Moderate KEYWORDS: quartiles 80. Referring to Table 3-3, the median number of vitamin supplements sold in this sample is . ANSWER: 26.5 TYPE: FI DIFFICULTY: Moderate KEYWORDS: median 81. Referring to Table 3-3, the range of the number of vitamin supplements sold in this sample is . ANSWER: 22 TYPE: FI DIFFICULTY: Easy KEYWORDS: range 82. Referring to Table 3-3, the interquartile range of the number of vitamin supplements sold in this sample is . ANSWER: 15 TYPE: FI DIFFICULTY: Moderate KEYWORDS: interquartile range 83. Referring to Table 3-3, the variance of the number of vitamin supplements sold in this sample is . ANSWER: 54.1 TYPE: FI DIFFICULTY: Easy KEYWORDS: variance 84. Referring to Table 3-3, the standard deviation of the number of vitamin supplements sold in this sample is . ANSWER: 7.4 TYPE: FI DIFFICULTY: Easy

80 Numerical Descriptive Measures KEYWORDS: standard deviation 85. Referring to Table 3-3, the coefficient of variation of the number of vitamin supplements sold in this sample is percent. ANSWER: 26.3% TYPE: FI DIFFICULTY: Moderate KEYWORDS: coefficient of variation 86. Referring to Table 3-3, the five-number summary of the data in this sample consists of , , , , . ANSWER: 19, 20, 26.5, 35, 41 TYPE: FI DIFFICULTY: Moderate KEYWORDS: five-number summary 87. Referring to Table 3-3, construct a box-and-whisker plot for the data in this sample. ANSWER: Box-and-whisker Plot

TYPE: PR DIFFICULTY: Moderate KEYWORDS: box-and-whisker plot 88. Referring to Table 3-3, what type of shape does the distribution of the sample appear to have? ANSWER: Slightly positive or right-skewed. TYPE: PR DIFFICULTY: Moderate KEYWORDS: shape TABLE 3-4 The stem-and-leaf display below represents the number of cargo manifests approved by customs inspectors of the Port of New York in a sample of 35 days. STEM LEAVES 1H 67889 2L 0011122223333444

Numerical Descriptive Measures 2H 3L

5566678899 1122

Note (1): 1H means the “high teens” – 15, 16, 17, 18, or 19; 2L means the “low twenties” – 20, 21, 22, 23, or 24; 2H means the “high twenties” – 25, 26, 27, 28, or 29, etc. Note (2): For this sample, the sum of the observations is 838, the sum of the squares of the observations is 20,684, and the sum of the squared differences between each observation and the mean is 619.89. 89. Referring to Table 3-4, the arithmetic mean of the customs data is

ANSWER: 23.9 TYPE: FI DIFFICULTY: Easy KEYWORDS: arithmetic mean 90. Referring to Table 3-4, the median of the customs data is

ANSWER: 23 TYPE: FI DIFFICULTY: Moderate KEYWORDS: median 91. Referring to Table 3-4, the first quartile of the customs data is

ANSWER: 21 TYPE: FI DIFFICULTY: Moderate KEYWORDS: quartiles 92. Referring to Table 3-4, the third quartile of the customs data is

ANSWER: 27 TYPE: FI DIFFICULTY: Moderate KEYWORDS: quartiles 93. Referring to Table 3-4, the range of the customs data is

ANSWER: 16 TYPE: FI DIFFICULTY: Easy KEYWORDS: range 94. Referring to Table 3-4, the interquartile range of the customs data is

ANSWER: 6 TYPE: FI DIFFICULTY: Moderate KEYWORDS: interquartile range 95. Referring to Table 3-4, the variance of the customs data is ANSWER:

82 Numerical Descriptive Measures 18.2 TYPE: FI DIFFICULTY: Easy KEYWORDS: variance 96. Referring to Table 3-4, the standard deviation of the customs data is

ANSWER: 4.3 TYPE: FI DIFFICULTY: Easy KEYWORDS: standard deviation 97. Referring to Table 3-4, the coefficient of variation of the customs data is

percent.

ANSWER: 17.8% or 18% TYPE: FI DIFFICULTY: Moderate KEYWORDS: coefficient of variation 98. Referring to Table 3-4, the five-number summary for the data in the customs sample consists of , , , , . ANSWER: 16, 21, 23, 27, 32 TYPE: FI DIFFICULTY: Moderate KEYWORDS: five-number summary 99. Referring to Table 3-4, construct a box-and-whisker plot of this sample. ANSWER: Box-and-whisker Plot

TYPE: PR DIFFICULTY: Moderate KEYWORDS: box-and-whisker plot TABLE 3-5 The rate of return of a Fortune 500 company over the past 15 years are: 3.17%, 4.43%, 5.93%, 5.43%, 7.29%, 8.21%, 6.23%, 5.23%, 4.34%, 6.68%, 7.14%, -5.56%, -5.23%, -5.73%, -10.34% 100.

Referring to Table 3-5, compute the arithmetic mean rate of return.

ANWER: 2.48%

Numerical Descriptive Measures

TYPE: PR DIFFICULTY: Easy KEYWORDS: arithmetic mean 101.

Referring to Table 3-5, compute the geometric mean rate of return.

ANWER: 2.31% TYPE: PR DIFFICULTY: moderate KEYWORDS: geometric mean rate of return 102.

Referring to Table 3-5, what is the range of the rate of return?

ANSWER: 18.55% TYPE: PR DIFFICULTY: Easy KEYWORDS: range 103.

Referring to Table 3-5, construct a box-and-whisker plot for the rate of return.

ANSWER: Box-and-whisker Plot

-0.15

-0.1

-0.05

0.05

0.1

TYPE: PR DIFFICULTY: Easy KEYWORDS: box-and-whisker plot 104.

Referring to Table 3-5, what is the shape of the distribution for the rate of return?

ANSWER: Left-skewed TYPE: PR DIFFICULTY: Easy KEYWORDS: shape TABLE 3-6 The rate of return of an Internet Service Provider over a 10 year period are: 10.25%, 12.64%, 8.37%, 9.29%, 6.23%, 42.53%, 29.23%, 15.25%, 21.52%, -2.35%. 105.

Referring to Table 3-6, compute the arithmetic mean rate of return.

ANWER: 15.30% TYPE: PR DIFFICULTY: Easy KEYWORDS: arithmetic mean 106.

Referring to Table 3-6, compute the geometric mean rate of return.

84 Numerical Descriptive Measures

ANSWER: 14.68% TYPE: PR DIFFICULTY: Moderate KEYWORDS: geometric mean rate of return 107.

Referring to Table 3-6, construct a box-and-whisker plot for the rate of return

ANWER: Box-and-whisker Plot

-0.1

0.1

0.2

0.3

0.4

0.5

TYPE: PR DIFFICULTY: Moderate KEYWORDS: box-and-whisker plot 108.

Referring to Table 3-6, what is the shape of the distribution for the rate of return?

ANSWER: Right-skewed TYPE: PR DIFFICULTY: Moderate KEYWORDS: shape

109. The Z scores can be used to identify outliers. ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: Z scores

110. The larger the Z score, the farther is the distance from the observation to the median. ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: Z scores

111. As a general rule, an observation is considered an extreme value if its Z score is greater than −3.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: Z score

112. As a general rule, an observation is considered an extreme value if its Z score is greater than 3. ANSWER:

Numerical Descriptive Measures

True TYPE: TF DIFFICULTY: Easy KEYWORDS: Z score

113. As a general rule, an observation is considered an extreme value if its Z score is less than 3. ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: Z score

114. As a general rule, an observation is considered an extreme value if its Z score is less than −3. ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: Z score

115. The Z score of an observation can never be negative. ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: Z score

116. The Z score of an observation measures how many standard deviations is the value from the mean. ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: Z score

117. The 12-month rate of returns over a nine year period of a particular stock is 0.099, −0.289, 0.089, 0.226, 0.041, 0.161, 0.064, −0.029 and 0.022. The geometric mean rate of return for this stock is . ANSWER: 3.23% or 0.0323 TYPE: FI DIFFICULTY: moderate KEYWORDS: geometric mean rate of return

118. The rate of return for the S&P 500 over a seven year period is −0.029, −0.061, −0.493, −0.286, −0.160, −0.186 and −0.224. The geometric mean rate of return is

ANSWER: −22.03% or −0.2203 TYPE: FI DIFFICULTY: moderate KEYWORDS: geometric mean rate of return

119. The rate of return for Microsoft’s stock over a seven year period is 0.527, 0.145, 0.684, 1.146, 0.564, 0.883 and 0.436. The geometric mean rate of return is

86 Numerical Descriptive Measures

ANSWER: 59.90% or 0.5990 TYPE: FI DIFFICULTY: moderate KEYWORDS: geometric mean rate of return TABLE 3-7 Given below is the frequency distribution of the 12-month rate of return achieved by 30 stocks. 12-month Rate of Return −0.10 but less than 0.0 0.0 but less than 0.1 0.1 but less than 0.2 0.2 but less than 0.3 0.3 but less than 0.4

Number of Funds 3 5 6 10 6

120. Referring to Table 3-7, what is the approximate mean rate of return? ANSWER: 0.1867 TYPE: PR DIFFICULTY: Moderate KEYWORDS: approximate mean

121. Referring to Table 3-7, what is the approximate variance? ANSWER: 0.0162 TYPE: PR DIFFICULTY: Moderate KEYWORDS: approximate variance

122. Referring to Table 3-7, what is the approximate standard deviation? ANSWER: 0.1273 TYPE: PR DIFFICULTY: Moderate KEYWORDS: approximate standard deviation TABLE 3-8 Given below is the frequency distribution of the number of defective tomatoes in 50 different shipments. Defective Items 0 but less than 5 5 but less than 10 10 but less than 15 15 but less than 20 20 but less than 25 25 but less than 30

Frequency 35 7 5 2 1 0

Numerical Descriptive Measures

123. Referring to Table 3-8, what is the approximate mean number of defective tomatoes? ANSWER: 5.2 TYPE: PR DIFFICULTY: Moderate KEYWORDS: approximate mean 124.

Referring to Table 3-8, what is the approximate variance?

ANSWER: 23.6837 TYPE: PR DIFFICULTY: Moderate KEYWORDS: approximate variance 125.

Referring to Table 3-8, what is the approximate standard deviation?

ANSWER: 4.8666 TYPE: PR DIFFICULTY: Moderate KEYWORDS: approximate standard deviation

Basic Probability

CHAPTER 4: BASIC PROBABILITY 1. If two events are collectively exhaustive, what is the probability that one or the other occurs? a) 0 b) 0.50 c) 1.00 d) Cannot be determined from the information given. ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: collectively exhaustive 2. If two events are collectively exhaustive, what is the probability that both occur at the same time? a) 0 b) 0.50 c) 1.00 d) Cannot be determined from the information given. ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: collectively exhaustive, mutually exclusive EXPLANATION: We do not know if they are mutually exclusive. 3. If two events are mutually exclusive, what is the probability that one or the other occurs? a) 0 b) 0.50 c) 1.00 d) Cannot be determined from the information given. ANSWER: d TYPE: MC DIFFICULTY: moderate KEYWORDS: collectively exhaustive, mutually exclusive EXPLANATION: We do not know if they are collectively exhaustive. 4. If two events are mutually exclusive, what is the probability that both occur at the same time? a) 0 b) 0.50 c) 1.00 d) Cannot be determined from the information given. ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: mutually exclusive 5. If two events are mutually exclusive and collectively exhaustive, what is the probability that both occur?

Basic Probability a) 0 b) 0.50 c) 1.00 d) Cannot be determined from the information given. ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: collective exhaustive, mutually exclusive 6. If two events are mutually exclusive and collectively exhaustive, what is the probability that one or the other occurs? a) 0 b) 0.50 c) 1.00 d) Cannot be determined from the information given. ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: collectively exhaustive, mutually exclusive 7. If events A and B are mutually exclusive and collectively exhaustive, what is the probability that event A occurs? a) 0 b) 0.50 c) 1.00 d) Cannot be determined from the information given. ANSWER: d TYPE: MC DIFFICULTY: moderate KEYWORDS: collectively exhaustive, mutually exclusive EXPLANATION: We do not know if they are equally likely events. 8. If two equally likely events A and B are mutually exclusive and collectively exhaustive, what is the probability that event A occurs? a) 0 b) 0.50 c) 1.00 d) Cannot be determined from the information given. ANSWER: b TYPE: MC DIFFICULTY: easy KEYWORDS: collectively exhaustive, mutually exclusive 9. If two equally likely events A and B are mutually exclusive, what is the probability that event A occurs? a) 0 b) 0.50 c) 1.00 d) Cannot be determined from the information given.

Basic Probability

ANSWER: d TYPE: MC DIFFICULTY: moderate KEYWORDS: collectively exhaustive, mutually exclusive EXPLANATION: We do not know if they are collectively exhaustive. 10. If two equally likely events A and B are collectively exhaustive, what is the probability that event A occurs? a) 0 b) 0.50 c) 1.00 d) Cannot be determined from the information given. ANSWER: d TYPE: MC DIFFICULTY: moderate KEYWORDS: collectively exhaustive, mutually exclusive EXPLANATION: We do not know if they are mutually exclusive. 11. Selection of raffle tickets from a large bowl is an example of a) sampling with replacement. b) sampling without replacement. c) subjective probability. d) None of the above. ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: sampling with replacement, sampling without replacement 12. If two events are independent, what is the probability that they both occur? a) 0 b) 0.50 c) 1.00 d) Cannot be determined from the information given. ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: statistical independence

13. If the outcome of event A is not affected by event B, then events A and B are said to be a) b) c) d)

mutually exclusive. statistically independent. collectively exhaustive. None of the above.

ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: statistical independence

14. If event A and event B cannot occur at the same time, then events A and B are said to be

Basic Probability a) b) c) d)

mutually exclusive. statistically independent. collectively exhaustive. None of the above.

ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: mutually exclusive

15. If either event A or event B must occur, then events A and B are said to be a) b) c) d)

mutually exclusive. statistically independent. collectively exhaustive. None of the above.

ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: collectively exhaustive 16. The collection of all possible events is called a) a simple probability. b) a sample space. c) a joint probability. d) the null set. ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: sample space 17. All the events in the sample space that are not part of the specified event are called a) simple events. b) joint events. c) the sample space. d) the complement of the event. ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: sample space, complement 18. Simple probability is also called a) marginal probability. b) joint probability. c) conditional probability. d) Bayes' theorem. ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: marginal probability

Basic Probability

19. When using the general multiplication rule, P(A and B) is equal to a) P(A|B)P(B). b) P(A)P(B). c) P(B)/P(A). d) P(A)/P(B). ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: multiplication rule 20. A business venture can result in the following outcomes (with their corresponding chance of occurring in parentheses): Highly Successful (10%), Successful (25%), Break Even (25%), Disappointing (20%), and Highly Disappointing (?). If these are the only outcomes possible for the business venture, what is the chance that the business venture will be considered Highly Disappointing? a) 10% b) 15% c) 20% d) 25% ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: marginal probability 21. A recent survey of banks revealed the following distribution for the interest rate being charged on a home loan (based on a 30-year mortgage with a 10% down payment). Interest Rate Probability

7.0% 0.12

7.5% 0.23

8.0% 0.24

8.5% 0.35

> 8.5% 0.06

If a bank is selected at random from this distribution, what is the chance that the interest rate charged on a home loan will exceed 8.0%? a) 0.06 b) 0.41 c) 0.59 d) 1.00 ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: marginal probability, addition rule 22. The employees of a company were surveyed on questions regarding their educational background and marital status. Of the 600 employees, 400 had college degrees, 100 were single, and 60 were single college graduates. The probability that an employee of the company is single or has a college degree is: a) 0.10. b) 0.25. c) 0.667. d) 0.733.

Basic Probability ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: addition rule 23. The employees of a company were surveyed on questions regarding their educational background and marital status. Of the 600 employees, 400 had college degrees, 100 were single, and 60 were single college graduates. The probability that an employee of the company is married and has a college degree is: a) 40/600. b) 340/600. c) 400/600. d) 500/600. ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: joint probability 24. The employees of a company were surveyed on questions regarding their educational background and marital status. Of the 600 employees, 400 had college degrees, 100 were single, and 60 were single college graduates. The probability that an employee of the company does not have a college degree is: a) 0.10. b) 0.33. c) 0.67. d) 0.75. ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: complement 25. The probability that house sales will increase in the next 6 months is estimated to be 0.25. The probability that the interest rates on housing loans will go up in the same period is estimated to be 0.74. The probability that house sales or interest rates will go up during the next 6 months is estimated to be 0.89. The probability that both house sales and interest rates will increase during the next 6 months is: a) 0.10. b) 0.185. c) 0.705. d) 0.90. ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: joint probability 26. The probability that house sales will increase in the next 6 months is estimated to be 0.25. The probability that the interest rates on housing loans will go up in the same period is estimated to be 0.74. The probability that house sales or interest rates will go up during the next 6 months is estimated to be 0.89. The probability that neither house sales nor interest rates will increase during the next 6 months is:

Basic Probability

a) 0.11. b) 0.195. c) 0.89. d) 0.90. ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: joint probability, complement 27. The probability that house sales will increase in the next 6 months is estimated to be 0.25. The probability that the interest rates on housing loans will go up in the same period is estimated to be 0.74. The probability that house sales or interest rates will go up during the next 6 months is estimated to be 0.89. The probability that house sales will increase but interest rates will not during the next 6 months is: a) 0.065. b) 0.15. c) 0.51. d) 0.89. ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: joint probability, complement 28. The probability that house sales will increase in the next 6 months is estimated to be 0.25. The probability that the interest rates on housing loans will go up in the same period is estimated to be 0.74. The probability that house sales or interest rates will go up during the next 6 months is estimated to be 0.89. The events of increase in house sales and increase in interest rates in the next 6 months are a) statistically independent. b) mutually exclusive. c) collectively exhaustive. d) None of the above. ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: joint probability, statistical independence EXPLANATION: They are not statistically independent. 29. The probability that house sales will increase in the next 6 months is estimated to be 0.25. The probability that the interest rates on housing loans will go up in the same period is estimated to be 0.74. The probability that house sales or interest rates will go up during the next 6 months is estimated to be 0.89. The events of increase in house sales and no increase in house sales in the next 6 months are a) statistically independent. b) mutually exclusive. c) collectively exhaustive. d) (B) and (C) ANSWER: d

Basic Probability TYPE: MC DIFFICULTY: Moderate KEYWORDS: mutually exclusive, collectively exhaustive, complement 30. The probability that a new advertising campaign will increase sales is assessed as being 0.80. The probability that the cost of developing the new ad campaign can be kept within the original budget allocation is 0.40. Assuming that the two events are independent, the probability that the cost is kept within budget and the campaign will increase sales is: a) 0.20. b) 0.32. c) 0.40. d) 0.88. ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: statistical independence, joint probability, multiplication rule 31. The probability that a new advertising campaign will increase sales is assessed as being 0.80. The probability that the cost of developing the new ad campaign can be kept within the original budget allocation is 0.40. Assuming that the two events are independent, the probability that the cost is kept within budget or the campaign will increase sales is: a) 0.20. b) 0.32. c) 0.68. d) 0.88. ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: statistical independence, multiplication rule, addition rule 32. The probability that a new advertising campaign will increase sales is assessed as being 0.80. The probability that the cost of developing the new ad campaign can be kept within the original budget allocation is 0.40. Assuming that the two events are independent, the probability that the cost is not kept within budget or the campaign will not increase sales is: a) 0.12. b) 0.32. c) 0.68. d) 0.88. ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: statistical independence, multiplication rule, addition rule, complement 33. The probability that a new advertising campaign will increase sales is assessed as being 0.80. The probability that the cost of developing the new ad campaign can be kept within the original budget allocation is 0.40. Assuming that the two events are independent, the probability that neither the cost is kept within budget nor the campaign will increase sales is: a) 0.12. b) 0.32. c) 0.68.

Basic Probability

d) 0.88. ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: statistical independence, multiplication rule, joint probability, complement 34. According to a survey of American households, the probability that the residents own 2 cars if annual household income is over $25,000 is 80%. Of the households surveyed, 60% had incomes over $25,000 and 70% had 2 cars. The probability that the residents of a household own 2 cars and have an income over $25,000 a year is: a) 0.12. b) 0.18. c) 0.22. d) 0.48. ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: joint probability, conditional probability 35. According to a survey of American households, the probability that the residents own 2 cars if annual household income is over $25,000 is 80%. Of the households surveyed, 60% had incomes over $25,000 and 70% had 2 cars. The probability that the residents of a household do not own 2 cars and have an income over $25,000 a year is: a) 0.12. b) 0.18. c) 0.22. d) 0.48. ANSWER: a TYPE: MC DIFFICULTY: Difficult KEYWORDS: joint probability, complement, multiplication rule, conditional probability 36. According to a survey of American households, the probability that the residents own 2 cars if annual household income is over $25,000 is 80%. Of the households surveyed, 60% had incomes over $25,000 and 70% had 2 cars. The probability that the residents of a household own 2 cars and have an income less than or equal to $25,000 a year is: a) 0.12. b) 0.18. c) 0.22. d) 0.48. ANSWER: c TYPE: MC DIFFICULTY: Difficult KEYWORDS: joint probability, complement, multiplication rule, conditional probability 37. According to a survey of American households, the probability that the residents own 2 cars if annual household income is over $25,000 is 80%. Of the households surveyed, 60% had incomes

100 Basic Probability over $25,000 and 70% had 2 cars. The probability that annual household income is over $25,000 if the residents of a household own 2 cars is: a) 0.42. b) 0.48. c) 0.50. d) 0.69. ANSWER: d TYPE: MC DIFFICULTY: Difficult KEYWORDS: conditional probability, Bayes’ theorem 38. According to a survey of American households, the probability that the residents own 2 cars if annual household income is over $25,000 is 80%. Of the households surveyed, 60% had incomes over $25,000 and 70% had 2 cars. The probability that annual household income is over $25,000 if the residents of a household do not own 2 cars is: a) 0.12. b) 0.18. c) 0.40. d) 0.70. ANSWER: c TYPE: MC DIFFICULTY: Difficult KEYWORDS: conditional probability, complement, Bayes’ theorem 39. According to a survey of American households, the probability that the residents own 2 cars if annual household income is over $25,000 is 80%. Of the households surveyed, 60% had incomes over $25,000 and 70% had 2 cars. The probability that the residents do not own 2 cars if annual household income is not over $25,000 is: a) 0.12. b) 0.18. c) 0.45. d) 0.70. ANSWER: c TYPE: MC DIFFICULTY: Difficult KEYWORDS: conditional probability, complement 40. A company has 2 machines that produce widgets. An older machine produces 23% defective widgets, while the new machine produces only 8% defective widgets. In addition, the new machine produces 3 times as many widgets as the older machine does. Given that a widget was produced by the new machine, what is the probability it is not defective? a) 0.06 b) 0.50 c) 0.92 d) 0.94 ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: conditional probability, complement

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101

41. A company has 2 machines that produce widgets. An older machine produces 23% defective widgets, while the new machine produces only 8% defective widgets. In addition, the new machine produces 3 times as many widgets as the older machine does. What is the probability that a randomly chosen widget produced by the company is defective? a) 0.078 b) 0.1175 c) 0.156 d) 0.310 ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: marginal probability 42. A company has 2 machines that produce widgets. An older machine produces 23% defective widgets, while the new machine produces only 8% defective widgets. In addition, the new machine produces 3 times as many widgets as the older machine does. Given a randomly chosen widget was tested and found to be defective, what is the probability it was produced by the new machine? a) 0.08 b) 0.15 c) 0.489 d) 0.511 ANSWER: d TYPE: MC DIFFICULTY: Difficult KEYWORDS: conditional probability, Bayes’ theorem TABLE 4-1 Mothers Against Drunk Driving is a very visible group whose main focus is to educate the public about the harm caused by drunk drivers. A study was recently done that emphasized the problem we all face with drinking and driving. Four hundred accidents that occurred on a Saturday night were analyzed. Two items noted were the number of vehicles involved and whether alcohol played a role in the accident. The numbers are shown below:

Did alcohol play a role? Yes No Totals

Number of Vehicles Involved 1 2 3 50 100 20 25 175 30 75 275 50

Totals 170 230 400

43. Referring to Table 4-1, what proportion of accidents involved more than one vehicle? a) 50/400 or 12.5% b) 75/400 or 18.75% c) 275/400 or 68.75% d) 325/400 or 81.25% ANSWER: d

102 Basic Probability TYPE: MC DIFFICULTY: Easy KEYWORDS: contingency table, empirical classical probability, addition rule 44. Referring to Table 4-1, what proportion of accidents involved alcohol and a single vehicle? a) 25/400 or 6.25% b) 50/400 or 12.5% c) 195/400 or 48.75% d) 245/400 or 61.25% ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: contingency table, empirical classical probability, joint probability 45. Referring to Table 4-1, what proportion of accidents involved alcohol or a single vehicle? a) 25/400 or 6.25% b) 50/400 or 12.5% c) 195/400 or 48.75% d) 245/400 or 61.25% ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: contingency table, empirical classical probability, addition rule 46. Referring to Table 4-1, given alcohol was involved, what proportion of accidents involved a single vehicle? a) 50/75 or 66.67% b) 50/170 or 29.41% c) 120/170 or 70.59% d) 120/400 or 30% ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: contingency table, empirical classical probability, marginal probability 47. Referring to Table 4-1, given that multiple vehicles were involved, what proportion of accidents involved alcohol? a) 120/170 or 70.59% b) 120/230 or 52.17% c) 120/325 or 36.92% d) 120/400 or 30% ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: contingency table, empirical classical probability, conditional probability, addition rule 48. Referring to Table 4-1, given that 3 vehicles were involved, what proportion of accidents involved alcohol?

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103

a) 20/30 or 66.67% b) 20/50 or 40% c) 20/170 or 11.77% d) 20/400 or 5% ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: contingency table, empirical classical probability, conditional probability 49. Referring to Table 4-1, given that alcohol was not involved, what proportion of the accidents were single vehicle? a) 50/75 or 66.67% b) 25/230 or 10.87% c) 50/170 or 29.41% d) 25/75 or 33.33% ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: contingency table, empirical classical probability, conditional probability, complement 50. Referring to Table 4-1, given that alcohol was not involved, what proportion of the accidents were multiple vehicle? a) 50/170 or 29.41% b) 120/170 or 70.59% c) 205/230 or 89.13% d) 25/230 or 10.87% ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: contingency table, empirical classical probability, conditional probability, complement TABLE 4-2 An alcohol awareness task force at a Big-Ten university sampled 200 students after the midterm to ask them whether they went bar hopping the weekend before the midterm or spent the weekend studying, and whether they did well or poorly on the midterm. The following result was obtained. Studying for Exam Went Bar Hopping

Did Well on Midterm 80 30

Did Poorly on Midterm 20 70

51. Referring to Table 4-2, what is the probability that a randomly selected student who went bar hopping will do well on the midterm? a. 30/100 or 30% b. 30/110 or 27.27% c. 30/200 or 15% d. (100/200)*(110/200) or 27.50%

104 Basic Probability

ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: contingency table, empirical classical probability, conditional probability 52. Referring to Table 4-2, what is the probability that a randomly selected student did well on the midterm or went bar hopping the weekend before the midterm? a) 30/200 or 15% b) (80+30)/200 or 55% c) (30+70)/200 or 50% d) (80+30+70)/200 or 90% ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: contingency table, empirical classical probability, addition rule 53. Referring to Table 4-2, what is the probability that a randomly selected student did well on the midterm and also went bar hopping the weekend before the midterm? a) 30/200 or 15% b) (80+30)/200 or 55% c) (30+70)/200 or 50% d) (80+30+70)/200 or 90% ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: contingency table, empirical classical probability, joint probability 54. Referring to Table 4-2, the events "Did Well on Midterm" and "Studying for Exam" are a) statistically dependent. b) mutually exclusive. c) collective exhaustive. d) None of the above. ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: contingency table, empirical classical probability, statistical independence, joint probability 55. Referring to Table 4-2, the events "Did Well on Midterm" and "Studying for Exam" are a) not statistically dependent. b) not mutually exclusive. c) collective exhaustive. d) None of the above. ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: contingency table, empirical classical probability, mutually exclusive, joint probability 56. Referring to Table 4-2, the events "Did Well on Midterm" and "Did Poorly on Midterm" are

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105

a) statistically dependent. b) mutually exclusive. c) collective exhaustive. d) All of the above. ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: contingency table, empirical classical probability, statistical independence, mutually exclusive, collective exhaustive, joint probability

57. True or False: When A and B are mutually exclusive, P(A or B) can be found by adding P(A) and P(B). ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: mutually exclusive, addition rule 58. True or False: The collection of all the possible events is called a sample space. ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: sample space

59. True or False: If A and B cannot occur at the same time they are called mutually exclusive. ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: mutually exclusive

60. True or False: If either A or B must occur they are called mutually exclusive. ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: mutually exclusive, collective exhaustive

61. True or False: If either A or B must occur they are called collectively exhaustive. ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: collective exhaustive

62. True or False: If P(A) = 0.4 and P(B) = 0.6, then A and B must be collectively exhaustive. ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: collective exhaustive, mutually exclusive

106 Basic Probability

63. True or False: If P(A) = 0.4 and P(B) = 0.6, then A and B must be mutually exclusive. ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: mutually exclusive

64. True or False: If P(A or B) = 1.0, then A and B must be mutually exclusive. ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: mutually exclusive, collective exhaustive

65. True or False: If P(A or B) = 1.0, then A and B must be collectively exhaustive. ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: collective exhaustive

66. True or False: If P(A and B) = 0, then A and B must be mutually exclusive. ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: mutually exclusive

67. True or False: If P(A and B) = 0, then A and B must be collectively exhaustive. ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: collectively exhaustive, mutually exclusive

68. True or False: If P(A and B) = 1, then A and B must be collectively exhaustive. ANSWER: True TYPE: TF DIFFICULTY: Difficult KEYWORDS: collective exhaustive

69. True or False: If P(A and B) = 1, then A and B must be mutually exclusive. ANSWER: False TYPE: TF DIFFICULTY: Difficult KEYWORDS: mutually exclusive, collective exhaustive

70. Suppose A and B are independent events where P(A) = 0.4 and P(B) = 0.5. Then P(A and B) = . ANSWER:

Basic Probability

107

0.2 TYPE: FI DIFFICULTY: Easy KEYWORDS: statistical independence, multiplication rule

71. Suppose A and B are mutually exclusive events where P(A) = 0.4 and P(B) = 0.5. Then P(A and B) =

ANSWER: 0 TYPE: FI DIFFICULTY: Easy KEYWORDS: mutually exclusive, joint probability, multiplication rule

72. Suppose A and B are mutually exclusive events where P(A) = 0.4 and P(B) = 0.5. Then P(A or B) =

ANSWER: 0.9 TYPE: FI DIFFICULTY: Easy KEYWORDS: mutually exclusive, addition rule

73. Suppose A and B are independent events where P(A) = 0.4 and P(B) = 0.5. Then P(A or B) = . ANSWER: 0.7 TYPE: FI DIFFICULTY: Easy KEYWORDS: statistical independence, addition rule

74. Suppose A and B are events where P(A) = 0.4, P(B) = 0.5, and P(A and B) = 0.1. Then P(A or B) =

ANSWER: 0.8 TYPE: FI DIFFICULTY: Easy KEYWORDS: addition rule

75. Suppose A and B are events where P(A) = 0.4, P(B) = 0.5, and P(A and B) = 0.1. Then P(A|B) = . ANSWER: 0.2 TYPE: FI DIFFICULTY: Moderate KEYWORDS: conditional probability

76. Suppose A and B are events where P(A) = 0.4, P(B) = 0.5, and P(A and B) = 0.1. Then P(B|A) = . ANSWER: 0.25 TYPE: FI DIFFICULTY: Moderate KEYWORDS: conditional probability TABLE 4-3

108 Basic Probability

A survey is taken among customers of a fast-food restaurant to determine preference for hamburger or chicken. Of 200 respondents selected, 75 were children and 125 were adults. 120 preferred hamburger and 80 preferred chicken. 55 of the children preferred hamburger. 77. Referring to Table 4-3, the probability that a randomly selected individual is an adult is . ANSWER: 125/200 or 62.5% TYPE: FI DIFFICULTY: Moderate KEYWORDS: empirical classical probability, conditional probability, marginal probability 78. Referring to Table 4-3, the probability that a randomly selected individual is an adult or a child is . ANSWER: 200/200 or 100% TYPE: FI DIFFICULTY: Moderate KEYWORDS: empirical classical probability, addition rule 79. Referring to Table 4-3, the probability that a randomly selected individual is a child and prefers chicken is . ANSWER: 20/200 or 10% TYPE: FI DIFFICULTY: Moderate KEYWORDS: empirical classical probability, joint probability, multiplication rule 80. Referring to Table 4-3, the probability that a randomly selected individual is an adult and prefers chicken is . ANSWER: 60/200 or 30% TYPE: FI DIFFICULTY: Moderate KEYWORDS: empirical classical probability, joint probability, multiplication rule 81. Referring to Table 4-3, the probability that a randomly selected individual is a child or prefers hamburger is . ANSWER: 140/200 or 70% TYPE: FI DIFFICULTY: Moderate KEYWORDS: empirical classical probability, addition rule 82. Referring to Table 4-3, assume we know the person is a child. The probability that this individual prefers hamburger is . ANSWER: 55/75 or 73.33% TYPE: FI DIFFICULTY: Moderate KEYWORDS: empirical classical probability, conditional probability